Skip to main content

Full text of "Fundamental Studies in the Longitudinal Control of Automated Ground Vehicles"

■ft: 

GG2 

.A3 
no . 
FHiVA- 
RU- 



No. FHWA-RD-77-28 



i Pep tofTtaepflrtaw i 



/T^^jsJiMENTAL STUDIES IN THE LONGITUDINAt 
CONTROL OF AUTOMATED GROUND VEHICLES 



Library 



,^o^J^s^ 




^^ATES O'i 



December 1976 
Final Report 



Document is available to the public through 
the National Technical Information Service, 
Springfield, Virginia 22161 



Prepared for 

FEDERAL HIGHWAY ADMINISTRATION 
Offices of Research & Development 
Washington, D. C. 20590 



NOTICE 



This document is disseminated under the sponsorship of the 
Department of Transportation in the interest of information 
exchange. The United States Government assumes no liability 
for its contents or use thereof. 

The contents of this report reflect the views of the con- 
tracting organization, which is responsible for the facts and 
the accuracy of the data presented herein. The contents do 
not necessarily reflect the official views or policy of the 
Department of Transportation. This report does not consti- 
tute a standard, specification, or regulation. 

The United States Government does not endorse products or 
manufacturers. Trade or manufacturers' names appear herein 
only because they are considered essential to the object of 
this document. 



np- 



Technical Report Documentotion Page 



1. Rjp^rt No. 

FHWA-RD-77-28 



2. Governmen* Accession No. 



4. Title ond Subtitle 

Fundamental Studies in the Longitudinal Control 
of Automated Ground Vehicles 



7. Author's) 



R.E. Fenton, K.W. Olson, R.J. Mayhan, G.M. Takasaki 



3. Recipient's Cotolog No. 



5. Report Dote 

December 1976 



6. Performing Oraonization Code 



RF 4302 



8. Performing Organization Report No. 

RF 4302 Al-1 



Performing Organization Nome and Address 

Transportation Control Laboratory 
Department of Electrical Engineering 
The Ohio State University 
Columbus. Ohio 43210 



10. Work Unit No. (TRAIS) 



11. Contract or Gront No. 

DOT-FH-11-8874 



13. Type of Report ond Period Covered 



12. Sponsoring Agency Nome and Address 

Office of Research and Development 
^''^, J'ederal Highway Administration 
Department of Transportation 
Washington. D.C. 20590 



Final Report 
Aug. 1975 - Dec. 



1976 



14. 



15. Supplementary Notes 



FHWA Contract Manager: Fred Okano (HRS-32) 



16. Abstract 




Four essential aspects of the longitudinal control of vehicles in an 
automated, individual-vehicle system are considered here: a) Sector-level 
control; b) Communications between each controlled vehicle and the sector 
computer; c) The development of techniques for obtaining extremely accurate 
estimates of a vehicle's state; and d) The control of each individual 
vehicle. The emphasis was on the design, development and testing of 
hardware subsystems essential for implementing these facets in the context 
of high-speed (to 93 ft/sec or 28 ra/s), small time-headway (1-2 sec) 
operation. 

The accomplishments over the second year of a two-year study include: 
a) The development and field evaluation of techniques for obtaining accurate 
estimates of vehicle position and instantaneous speed — ± .05 ft in 10 ft 
(± .015m in 3.05m) and ± 0.7 ft/sec (± 0.21 m/s), respectively for one of 
the three approaches evaluated; b) The development of validated models for 
both the propulsion and braking dynamics of a typical U.S. sedan; c) The 
design and field testing of a vehicle controller which provided good tracking 
and a comfortable ride; and d) The specification of both minimal and 
realistic requirements for sector- level communications. 



17. Key Words 

Automatic highway, dual-mode, auto- 
matic longitudinal control, 
information source, sector communi- 
cations, sector computer. 



18. Distribution Statement 

This document is available to the 
public through the National Technical 
Information Service, Springfield, 
Virginia, 22161 



19. Security Clatsif. (o' this report) 

Unclassified 



20. Security Classif. (of this page) 

Unclassified 



21. No. of Pages 

192 



22. Pr 



■form DOT F 1700.7 (8-72) Reproduction of form and completed page is authorized 



FUNDAMENTAL STUDIES IN THE 
LONGITUDINAL CONTROL OF AUTOMATED GROUND VEHICLES 

EXECUTIVE SUMMARY 



The achievement of safe and efficient longitudinal control Is probably 
the most significant technical problem associated with Individual automated- 
vehicle, transport systems such as the automatic highway and automated guldeway 
transit. 

One general control structure would Involve a central controller to 
oversee network operations with this Including the coordination of sector- 
level computers— each of which would supervise and control the vehicles opera- 
ting In Its assigned sector. Four essential facets of operations at this 
sector level are: 

a) The specification and/or generation of vehicle 
command states; 

b) Communications between sector control and each 
controlled vehicle; 

c) The determination of the state of each vehicle; 
and 

d) The control of each Individual vehicle. 

The research reported here was performed during the second year of a 
two-year study, and It deals with the design, development and testing of 
hardware systems essential for Implementing these facets in the context of 
high-speed (to 93 ft/sec), small time-headway (1-2 sec) operation. 

Within this framework, the principal accomplishments over the second 
year of this study include; 

a) The development and field evaluation of a tech- 
nique, which involves the use of laterally 
positioned, current-carrying wires embedded in 
the roadway, for measuring vehicle position to 
within ±0.06 ft over the speed range 0-100 ft/sec; 

b) The development and laboratory testing of an 
approach anploying audio frequencies and heli- 
cally wound transmission lines for providing 
continuous absolute position information, within 
an accuracy of ±0.17 ft, to a string of moving 
vehicles; 

-ii- 



c) The use of a vehicle-borne radar and scattering 
enhancement plates embedded under the roadway 
surface to provide both an accurate position 
signal (e.g., a maximum position error of .05 
ft in a 10 ft-di stance), and an estimate of 
instantaneous velocity which is within ±.5 ft/ 
sec of the true value under all expected operating 
conditions over the speed range 0-100 ft/sec; 

d) The specification of both the propulsion- and 
braking dynamics of a "typical" U.S. passenger 
sedan, and a corresponding design of a vehicle 
controller for nonemergency operations; and 

e) The demonstration of controller performance on a 
roadway where position information was obtained 
from embedded current-carrying conductors and 

a vehicle-borne interpolator (This demonstration 
was successful in that a comfortable ride (|J| 
< 1.6 ft/sec3), an insensitivity to adverse 
environmental effects, and fairly good position 
control (±2 ft tracking errors) were achieved). 

Secondary accomplishments include: 

a) The specification of three general approaches to 
sector-level control, and the selection of one 
for further detailed study; 

b) The specification of both the minimal information 
transmission requirements for a sector computer- 
to-vehicle link, and the greatly increased require- 
ments when safety factors are given a paramont 
importance; and 

c) The specification of the accuracies to be expected, 
in measuring both position and instantaneous 
velocity, with a fifth wheel. 

Future efforts will be focused on the development of a 4 -mile sector wherein 
vehicles would be controlled via a sector computer located at roadside. 



■Ill- 



TABLE OF CONTENTS 



EXECUTIVE SUMMARY ii 

FIGURES vii 

TABLES. xii 

Chapter 

I . INTRODUCTION 1 

A. Introduction.. 1 

B. Dual -Mode System Concept 2 

C. Dual-Mode Control Hierarchy 3 

D. Overview 6 

II. ON SECTOR COMPUTER OPERATIONS 8 

A. Introduction 8 

B. Sector Configuration 9 

C. Required Corranand Trajectories 10 

D . Approach 1 11 

E. Approach 2 27 

F. Approach 3 35 

G. Conclusions -. 38 

III. ON SECTOR-LEVEL COMMUNICATIONS 39 

A. Introduction 39 

B. Minimal Required Information Transmission Rates 39 

C. Encoding of the Command and Status Information 46 

D. Coding for Error-Detection and -Correction..... 52 

E. Synchroni zation 56 

-iv- 



Chapter (Cont.) 

F. Conclusions 57 

IV. INFORMATION SOURCES FOR LONGITUDINAL CONTROL 58 

A. Introduction 58 

B. Information Source 1 59 

C. Information Source 1— A Crossed-Wire Approach 59 

D. Information Source 1--A Helical Transmission-Line Approach 78 

E. Information Source 1— Scattering Enhancement Plates 85 

F. Information Source 1— A Fifth VJheel 94 

G. Information Source 2 101 

H. Conclusions 101 

V. ON THE IDENTIFICATION OF VEHICLE DYNAMICS 105 

A. Introduction 105 

B. A Model of Bra king/ Roadway- Interface Dynamics 105 

C. On Braking Controller Design 110 

D. Vehicle Propulsion Dynamics 112 

VI. A VEHICLE LONGITUDINAL CONTROLLER— DESIGN AND EVALUATION 120 

A. Introduction 1 20 

B. Controller Design 121 

C. Full-Scale Tests and Results 126 

VII. SUMMARY AND CONCLUSIONS 135 

A. Summary and Conclusions 135 

B. Future Efforts 138 

Appendices 

A. INSTRUMENTATION INSTALLED AT THE TRANSPORTATION RESEARCH 

CENTER OF OHIO 139 



-V- 



Appendices (Cont.) 

B. HELICAL TRANSMISSION LINES AS AN INFORMATION SOURCE 143 

A. Ideal Operation 143 

B. Deviations From Ideal Operation 150 

C. Experimental Verification 1 54 

C. ON THE IDENTIFICATION OF BRAKING DYNAMICS 162 

A. A Model of Braking/Roadway Interface Dynamics 162 

B. Identification of Model Parameters 164 

C. Experimental Apparatus 1 66 

D. Experimental Results—Dry- Pavement Conditions 167 

E. Experimental Results— Wet- Pavement Conditions 175 

F. Conclusions 178 

D. DIGITAL COMMAND GENERATION 182 

A. Introduction 182 

B . A Command Generator 182 

C. Integration of Conmiand and Information Source Signals... 188 

REFERENCES 1 90 



■VI- 



LIST OF FIGURES 



Number 

1. One network control configuration 5 

2. The basic elements of a sector-level control configuration 5 

3. A simple sector configuration 9 

4. Computer architecture for Approach 1 13 

5. Typical moveup velocity trajectory 16 

6. Trajectories employed in moveup/moveback maneuvers 17 

7. Computer architecture for Approach 2 28 

8. Quantization of a command-acceleration merging trajectory 34 

9. Computer architecture for Approach 3 ^ 37 

10. A typical probability density function 44 

n. The worst-case failure if the acceleration bounds 

are not exceeded 49 

12. A discrete element, information source with position 
interpolation 60 

13. Top view of a spatially periodic wire configuration 62 

14. The relationship of two vertically mounted, sensing 

coils to the laterally positioned wires 62 

15. A block diagram of the signal processing employed with 

the "crossed-wire" approach 63 

16. An empirically determined choice for F(x, 0, .34) 64 

17. Voltages induced in the phase-reversal sensing coil 67 

18. Measured position error 70 

19. A theoretical block diagram of the state estimator 73 

20. Reconstruction of X + ex - X 75 



-vii- 



Figures (Cont.) 

Figure 

21. One possible realization of the state estimator 77 

22. Theoretical phase-difference versus the longitudinal 

coordinate 79 

23. Proposed longitudinal information source using two 

helically wound transmission lines 79 

24. Line placement and the region of allowed probe location 81 

25. Upper bound on the phase-difference error versus line 

separati on 82 

25. Interval for velocity estimation (elapsed time T) 84 

27. Behavior of vehicle-mounted Doppler radar with 

enhancement pi ates 86 

28. Low-speed, full-scale test data for Poppler radar with 
enhancement plates, 89 

29. One realization of velocity measurement 93 

30. Maximum measured error versus T--constant-speed case 93 

31. Measurement interval during a constant deceleration test 95 

32. Measurement interval for a vehicle decelerating at a 

constant rate 1 00 

33. A simple model of braking/roadway-interface dynamics 106 

34. Closed-loop system employed in the parameter-identification 
process , 1 07 

35. Comparison of vehicle response and model response for 
3 selected initial speeds and Ac = 14.5 ft/sec2 (Dry- 
pavement cond i ti ons ) 1 08 

36. KB6/a6 vs. Vq with Ac as a parameter 110 

37. Vehicle response for Vq = 40 ft/sec, Ac = 12.83 ft/sec^ 

and wet-pavement condi tions Ill 

38. Assumed full-scale response with an efficient anti-skid 
mode. (Vq = 40 ft/sec, Ac = 12.88 ft/sec2 and wet-pavement 

cond i ti ons ) Ill 

-viii- 



Figures (Cont.) 



Figure 



39. A velocity-dependent model of vehicle propulsion system/ 

roadway interface dynamics 113 

40 5(V) versus V (obtained from Reference 16) 115 

41. Velocity controller used for modeling 116 

42. Comparison of model and vehicle responses 117 

43. Kp(V) versus V 118 

44. y(V) versus V 118 

45. A more complex model 119 

46. General position controller.... 121 

47. A vehicle longitudinal control system 122 

48. A nonlinear compensator 124 

49. A Linear approximation of 1/Kp 125 

50. A piecewise-linear approximation of 1/Y 125 

51. Root-locus plot corresponding to Go(p) = 102K(p + 1.5)/ 

p2(p + 15)2 127 

52. Simulation responses (Xq - X) to a maneuvering command 

and a disturbance input 128 

53. The command qenerator and state estimator. 130 

54. The vehicle longitudinal controller 132 

A"! Instrumented section of roadway 140 

A-2 Installations under the roadway surface 141 

B-1 Two parallel wires with current 1 145 

B-2 Four parallel wires with currents I] and I2 145 

B-3 Proposed longitudinal reference system using two helically 

wound transmission 1 ines 147 

B-4 Coordinate system, probe location, and excitation for 

system shown in Figure B-3 148 



Figures (Cont.) 

Figure 

B-5 Theoretical phase-difference versus the longitudinal coordinate.... 149 

B-6 Geometry for the probe locations shifted Ax and Ay from 

desired location 1 52 

B-7 Phase angle 6-| which results from the addition of two phasors 154 

B-8 Amplitude of Hy versus distance from the line.(Ioh = 0.5) 155 

B-9 Variation in the phase of Hy for various positions in the 

cross-sectional plane. (Experimental resul ts) 1 57 

B-10 Variation in the phase of Hy for various positions in the 

cross-sectional plane. (Theoretical results) 158 

B-11 Phase-error {Bq) for various positions of the probes in the 

cross-sectional plane. (Experimental results) 159 

B-12 Phase-error (Se) for various positions of the probes in the 

cross-sectional plane. (Theoretical results).... 160 

B-13 An upper bound on the phase error (Be) for various positions 

of the probes in the cross-sectional plane 161 

C-1 A simple model of braking/roadway- interface dynamics 163 

C-2 Closed-loop system employed in the parameter-identification 

process 165 

C-3 Comparison of vehicle response and model response for 

3 selected initial speeds and A^ = 6.44 ft/sec2( Dry-pavement 

condi tions) 1 68 

C-4 Comparison of vehicle response and model response for 

3 selected initial speeds and A^ = 14.5 ft/sec2(Dry-pavement 

condi tions) 1 69 

C-5 Comparison of vehicle response and model response for 
V = Vj and V = V5 (Ac = 14.5 ft/sec2 and dry-pavement 
cond i ti ons ) 170 

C-5 Comparison of vehicle response and model response for V = Vj 

and V = V5(Ac = 14.5 ft/sec2 and dry-pavement conditions) 171 

C-6 KB6/aB vs. Vq with Ac as a parameter 174 

C-7 Comparison of vehicle and model responses for a high- 
gain control configuration (Vo = 60 ft/sec, Ac = 14.5 
ft/sec2, Gc * 2.0 and dry pavement) 176 

-X- 



Figures (Cont.) 



Figure 



C-8 Vehicle response under anti-skid conditions (Vq = 80 

ft/sec, Ac = 14.5 ft/sec2, Gc = 2 and dry pavement) 176 

C-9 Comparison of vehicle response and model response for 
3 selected initial speeds and Ac = 6.44 ft/sec2 (Wet- 
pavement conditions and V = Vj) 177 

C-10 Vehicle response for two selected initial speeds, 

Ac = 12.88 ft/sec2, V = V5 and wet-pavement conditions 179 

C-ll Assumed full-scale response with an efficient anti-skid mode 

(Vq = 40 ft/sec, Ac = 12.88 ft/sec2 and wet-pavement conditions) . .179 

C-12 Comparison between full-scale and model responses for 

V = V5, Ac = 9.66 ft/sec2, and wet-pavement 180 

D-1 Computer and control operations onboard a controlled vehicle 183 

P-2 A command acceleration profile and corresponding velocity 

and pos i t i on prof i 1 es 185 

D-3 One implementation of the Vc(nt) and Xc(nt) computations 187 

D-4 Implementation of AX* for a crossed-wire information 

source with position interpolation 189 



-XI- 



LIST OF TABLES 



Table 

I Basic Parameters 10 

II Permitted Operations 12 

III Information Requirements— Constant-Speed Operation 16 

IV Information Requirements— Online Maneuvering 21 

V Information Requirements— Mainline Speed Changes 22 

VI Information Requirements- -System Entry (Herging Operations) 23 

VII Information Requirements— Emergency Braking 24 

VIII Information Requirements— Emergency Braking (Modified Approach).... 25 

IX Summary of Information Storage Requirements 25 

X Summary of Information Storage Requirements (Approach II) 35 

XI Definition of Symbols 42 

XII Formulation of Minimal Code Word For Subchannel 1 47 

XIII Formulation of Minimal Code Word For Subchannel 2 47 

XIV Formulation of Minimal Code Word For Status Channel 50 

XV Formulation of Nominal Code Word For Subchannel 2 51 

XVI Formulation of Nominal Code Word For Status Link 52 

XVII Comparison of Several Random-Error Correcting Codes 54 

XVIII The Performance of Some Burst-Error Correcting Codes.. 55 

XIX Fifth-Wheel Data From Constant-Speed Tests 97 

XX Constant-Acceleration/Deceleration Tests 97 

XXI Model Parameters For Vw/Vj = Kb(p + 6)/p(p + a)(p + 8) 109 

C-I Model Parameters for Vw/V^ = Kb(p + 6)/p(p + a)(p + B) 173 



-Xll- 



^sti 



y * s - 



3 3 5 £ 
O" CT o- U 



^ § s 

3 &-g 



;: a a- o ■: 



c i« — -Q -O 
= 3 ra 3 3 
a. 7 C7> u u 



s 

E •" 



o * <^ ^ *** 
0(^^*0 



»- p^ V in 






— c 

- Q) 

E u 



3 3 3 U 
ff ff (T • 
M VI tn ^ 



E g' S 

s.-= g 



CO 

K 
O 



< 



a 



E 6 E 



8- 


-o*J 


- 


~ 


- 


rg 


o 

(0 - 


. 


. 




■ 


_o 


. 




o 


- 


O 




" 


o . 




■ 




o 








- 


o . 


— o 














o - 


_ o 




1 




- 






o . 


- o t 



ez 

llllllll 


zz 

nil 


nil 


IZ 

nil 


nil 


oz 

nil 


nil 


61 

nil 




8T 

III! 


nil 


nil 


nil 


91 

nil 


ini 


SI 

nil 


iin 


nil 


nil 


EI 

nil 


iin 


ZI 

ini 


iin 


II 

nil 


iiii 


01 

nil 


nil 


6 

nil 


111 


8 

IIII 


111! 


iiniiiii 


9 

Iin 


nil 


9 

IIII 


nil 


nil 


nil 


iiiiliiii 


z 

nil 


nil 


1 
iiiilini 



o 

H 

< 

O 
M 
W 



O 

u 



l'|T 'I'l'l' T|T T|T T|T T|T 'ITI' T|T TIT TIT TIT TIT TIT TIT TIT TIT TIT Tl'l 



1 inches 



o 



1^21 

S H S I 
u u E jc 



E M «) o 

f £ 2 I 



3 3 3 3 
W O" IT » 



)A o eo «o <a^ 
U3 o o (^ o 



E g- S 



EEE EE 



.2 E 

w 2 



E E £.= .= - ^ 



(A Ul O O O O 



\ 3 fsi 
IT) (fl CO 



3 3 3 3 

cr CT ff c 
in w n M 



3 5 £ 

o a V) 



C u & a* o o u 



ago 

S t~ ^ 



a- oi ^ >- 



>5 



Xlll 



CHAPTER I 
INTRODUCTION 



A. Introduction 

An examination of traffic conditions today— congested roadways, vehicle- 
related noise and pollution, a large number of accidents and fatalities, and 
poor service to large numbers of our population— indicates the need for improve- 
ment in our transportation system. Unfortunately, these conditions will be 
worse In the next few decades for it is widely predicted that both the number 
of vehicles and the miles traveled per vehicle will greatly increase. If one 
would look further ahead to the turn of the century, he would see vast sprawling 
superclties, with populations characterized by adequate Incomes, longer life 
spans, and Increased amounts of leisure time. One predictable result is greatly 
Increased travel. The resulting traffic situation could be chaotic, unless 
some dramatic Improvements are instituted beforehand. 

The solution to both the current and the anticipated future problems 
will be a combination of many approaches including perhaps the following: 
Improved high-speed rail systems; VTOL aircraft for short-distance trips; new 
and innovative mass transit systems; and the automation of various facets of 
individual ground transport. Here, the focus will be on the latter, wherein 
the suggested systems have generally fallen into three categories: 

1) Captive vehicle systems for use in restricted geogra- 
phical areas; 

2) Dual-mode systems for general coverage of urban areas; 
and 

3) Dual-mode systems for intercity automated highways. 

-1- 



The potential advantages associated with each category are well known and will 
only be briefly sunwnarized here. The first offers transportation to all citi- 
zens in a limited area— such as a downtown business district--and the partial 
or complete elimination of privately owned vehicles from that area with an 
attendant reduction in noise, air pollution, and congestion. The feasibility 
of this type of system is currently being evaluated via the operational captive- 
vehicle network at Morgantown, West Virginia.^ 

The general class of dual -mode systems offers the prospects of high flow 
capacities, enhanced vehicle safety, door-to-door movement in either a public 
conveyance, such as dial-a-bus, or in a privately owned vehicle, and extended 
mobility to the poor, the aged, and the infirm. The U.S. Department of Trans- 
portation had planned to develop a prototype dual-mode system by the early 
1980's;^ however, these plans are currently inactive. 

The initial studies on the automated highway were initiated in the 
late 1950's by General Motors Corporation,' and subsequently much effort was 
expended, both here and abroad, by various industrial organizations, government 
laboratories, and academic institutions.**"^' One ongoing effort is a cost- 
benefit analysis of various automated highway concepts by CALSPAN Corporation 
under the sponsorship of the Federal Highway Administration.^** 

An automated highway system would probably be first considered for an 
already congested network (e.g., the Northeast Corridor) because of its pros- 
pects for substantially increasing both flow capacity and highway safety. 
B. Dual -Mode System Concept 

The general dual-mode concept involves a roadway complex which consists 
of both automated and nonautomated roads. Various main arteries would probably 
be equipped for automation while various secondary streets/roads would not be 

-2- 



equipped. Ultimately, it would be expected that public vehicles and both indivi- 
dual private vehicles and commercial traffic would use the system-, however, it 
seems likely that initially only mass transit vehicles would be employed. 

An individual vehicle would enter the system at a special entrance point 
where it would first undergo a rapid automatic checkout, and the driver would 
indicate his destination. If it "passed" the checkout, the vehicle would move 
to an entrance ramp from which it would be automatically merged into the traffic 
stream. However, if it "failed" the vehicle would not be allowed to merge into 
the traffic stream; instead, it would be rejected and guided to a nearby service 
facility for repair. 

The traffic stream velocity would be fixed by a central traffic controller 
and would be dependent on weather, roadway conditions, the state of the traffic 
stream, etc. Once in the traffic stream, the vehicle would remain under auto- 
matic control until the driver's preselected exit were reached. Then the vehicle 
would be guided off the roadway onto an exit ramp, and control v/ould be returned 
to the driver. 

In the event of vehicle disability, the vehicle would be ejected from 
the main traffic stream. If it were controllable, it would be routed to the 
nearest emergency exit. If it were not, the use of one lane would be lost until 
the vehicle could be moved off the roadway. Hence, it would be temporarily 
necessary to direct the mainstream vehicles around the disabled one. Clearly, 
some provision must be made for clearing the roadway as quickly as possible. 
C. Dual -Mode Control Hierarchy 

The control required for the automated part of a dual -mode system is 
comprised of two intimately related facets. The first, macro-control, embodies 
the entire hierarchy of control which is necessary for system coordination. 
This is, of course, the "systems" level of control, and it includes such 

-3- 



operations as vehicle scheduling and routing, the determination and specification 
of traffic speeds, and system response to abnormal and emergency situations. 
The second facet, micro- control, is explicitly concerned with individual vehicle 
position regulation and maneuvering and encompasses both vehicle lateral control 
and longitudinal control. 

One general control hierarchy is shown in Fig. 1, where a central com- 
puter is shown as overseeing network operations. This task includes the 
coordination of individual sector computers— one of which is assigned to super- 
vise and control the vehicles operating in each network sector. Depending 
upon the size and complexity of a network, it might be desirable to have an 
additional level (s) of control in this hierarchy (i.e., a central computer to 
oversee network operations and to coordinate individual regional computers- 
each of which would, in turn, supervise several sector-level computers). 

Note from Fig. 2 that a sector-level, control configuration would be 
comprised of four basic elements; 
i) A sector computer; 

ii) A communication link for achieving both computer- 
to-vehicle and vehicle- to-computer transmissions; 
iii) An information source for directly providing the 
computer with state information on each vehicle; 
iv) An information source embedded in, or located 
nearby, the guldeway and intended to supply 
state information to each controlled vehicle. 
With this general configuration, the sector computer would have two 
independent indications of the state of each vehicle— one from the guideway- 
to-sector computer information source and one transmitted from the vehicle. 

-ft- 



(rr—f^ Vr—c? I xr—o^ xr—& I ^^cr—^ (r— 9 



V 



I 



y\. 



A 
Sector 
Control 



^\. 



B 
Sector 
Control 

zzu — 



^ 



c 

Sector 
Control 



Central 
Control 



Fig, 1 One network control confiquration. 




communication links 



status 



command 



^ 



X 6 X o 



n 



O X 



i I i i i 



SECTOR 
COMPUTER 



To Central Control 



o- Information 
source i 

X -Information 
source 2 



Fig. 2 The basic elements of a sector-level 
control configuration. 



-5- 



This would provide desired redundancy. Further, if the information received 
were of sufficient accuracy and timeliness, the system could be designed for 
a quick response to an anomalous situation. It may be noted that the confi- 
guration of Fig. 2 could be employed in conjunction with either a synchronous, 
an asynchronous, or a quasi-synchronous control strategy. 
D. Overview 

During the past two years, the Ohio State University has investigated 
various facets of sector-level longitudinal control with an emphasis on high- 
speed (up to 88 ft/sec) operation at time headways as small as 1 sec* During the 
first year, the principal focus was directed toward: 

1) A laboratory study of practically implementable 

information source configurations; and 
ii) The identification of vehicle longitudinal dyna- 
mics, the design of a vehicle controller based on 
those dynamics, and a field- test evaluation of 
the designed controller. 
A detailed description of these efforts is contained in Reference 16. 

During the second year of this investigation, the primary focus was 
on the following: 

i) Field and laboratory evaluations of 3 selected 
information source configurations, and the 
implementation of two of these in a field- test 
facility; 



* In a previous study, a reference system/vehicle-controller combina- 
tion for automatic lateral control was designed and tested under full-scale 
conditions. This effort was quite successful and demonstrated that excellent 
automatic lateral control could be achieved.*^ 

-6- 



ii) The identification of a vehicle's braking dyna- 
mics, the development of a refined model of 
vehicle propulsion system/roadway-interface 
dynamics, and the design of a vehicle controller 
for use with one developed information source con- 
figuration; and 
iii) Full-scale testing and evaluation of an infor- 
mation source/vehicle-controller combination. 
A secondary focus was an overview of: 

i) Sector-computer operations; and 
ii) Sector computer-to-control led vehicle 
communications. 
A fairly intensive survey of the accomplishments during this year are contained 
in the following chapters, and various detailed findings are included in the 
attached appendices. 



I 



-7- 



CHAPTER II 
ON SECTOR COMPUTER OPERATIONS 



A. Introduction 

As a first step toward specifying the requirements of a sector-level 
computer, three general approaches to sector-level computer operations are 
examined. In this analysis, it is assumed that the trajectory of each vehicle 
in a sector is specified by a higher-level control (e.g., a regional controller) 
and communicated to the sector computer. Subsequently, the latter would pro- 
vide each controlled vehicle with appropriate longitudinal reference information 
(e.g., its desired position and desired speed versus time).* 

The approaches considered are defined as follows: 
Approach #1. All permitted trajectories (position (Xc(t)) and 
speed (Vc(t)) would be stored in memory at sector 
level, and these would be recalled from memory as 
required and transmitted to each controlled vehicle. 
Approach #2. All allowed acceleration (A^) trajectories would 
be stored in memory. When a specified position/ 
velocity trajectory were required, the corres- 
ponding Aq trajectory would be recalled from memory 
and processed at the sector level to provide the 
required Vq and X^ information. The latter would 
be transmitted to a controlled vehicle. 



* In a subsequent study, it may be desirable to consider the case 
where each vehicle's trajectory is specified at the sector level. This would 
result in a requirement for more computer processing capability at the sector 
level than is specified here. 

-8- 



Approach #3. All permitted Aq trajectories would be stored onboard 
each vehicle, and the required processing to obtain 
Vc and X^. would be accomplished onboard. 
This listing is not intended to be all-inclusive and other approaches, which 
are possibly more suitable, can readily be defined. 
B. Sector Configuration 

In this preliminary analysis, there was no convincing reason for selecting 
a sector composed of complex geometries — especially since reasonable estimates 
of various parameters could be obtained from a relatively simple configuration. 

The selected geometries are shown in Fig. 3. These consist of a single, 
mainline lane of one-way traffic and a merging lane from which vehicles can 
merge onto the mainline. For reasons of convenience, it will be assumed that 
the sector shown in Fig. 3 is characterized by the parameters listed in Table 
I. These are probably typical of what might be expected in practice and, at 
the very least, correspond to those tentatively selected for a planned OSU 
facility at East Liberty, Ohio. 



-F 



Mainline 



±1 



Entry point 



iz 




Merging ranrip 



X3=0 



Fig. 3 A simple sector configuration. 



^s"^s 



The symbol Xj is used to represent a longitudinal position within a 

sector. Thus, as shown in Fig. 3, Xs = corresponds to the beginning of a 

sector and Xc = Le to the end. 

-9- 



TABLE I 
BASIC PARAMETERS 



Quanti ty 


Symbol 


Value 


Sector Length 


Ls 


3280 ft 


Communication Interval 


Tc 


100 m sec 


Maximum Speed 


Vax 


93 ft/sec 


Maneuvering Acceleration 


^0 


3.22 ft/sec^ 


Design Time Headway 


Ht 


1 sec 


Position Quantization 


AX 


0.05 ft 



C. Required Command Trajectories 

It presently appears as if trajectories for the following would be 
necessary: 

i) Constant-speed operation, 
ii) Mainline maneuvering (moveup-moveback). 
iii) Mainline speed changes, 
iv) System entry (merging operations), 
v) Emergency braking, 
vi) System startup (after a shutdown of mainline traffic). 

The parameters associated with each operation are listed in Table II. For 
example, constant-speed operation would be at one of four speeds— 30, 45, 60, 
or 88 ft/sec. These, and the other selections specified in this table, are 
believed to be typical of what would be required in practice. 

The command sent to a vehicle, for example Vehicle i, is represented 
via the following notation: 

Xci(I^T) = The command position of Vehicle i at t = KT. 

-10- 



Vci(KT) = The command speed of Vehicle i at t = KT. 
Acl(KT) = The command acceleration of Vehicle i at t = KT. 
The state of that vehicle is represented by 

Xi(KT) = The position of Vehicle i at t = KT. 
Vi(KT) = The speed of Vehicle i at t = KT. 
Ai(KT) = The acceleration of Vehicle i at t = KT. 
D. Approach 1 

a) Computer Architecture 

Consider the computer architecture shown in Fig. 4. It is comprised 
of the following primary parts: 

i) A central processing unit (CPU); 
ii) Address registers; 
iii) Multiplexing (MUX) units; 
iv) A permanent memory (ROM); and 
v) Output devices. 
There would be two general inputs to the CPU--one comprising the command 
information for each vehicle in the sector, and the second, status information 
from both each vehicle and Information Source 2. The former would be employed 
to select an addressing sequence for each vehicle which would be used to obtain, 
via a multiplexer, the corresponding Vc(t) and Xc(t) from the permanent memory.* 
Note that this information would be sent to two locations— to the appropriate 
controlled vehicle via a communication link and back to the CPU for checking 
purposes. 



* The sequence for a given vehicle would be changed if it were sub- 
sequently necessary to modify the specified operation. 

-11- 



TABLE II 
PERMITTED OPERATIONS 



Operation 


Symbols 




Parameter Range 


Constant Speed 


Vs 




30 ft/sec 
45 ft/sec 
60 ft/ sec 
88 ft/ sec. 




Mainline Maneuvering 
(ao = 3.22 ft/sec2) 


Vs. -AVri 
+AV-2 




30 ft/ sec. 


-7.5 ft/sec 
+7.5 ft/sec 


( 


f Cm 

(See Fig. 


3) 


45 ft/sec, 
60 ft/sec, 
88 ft/sec. 


-7.5 ft/sec 
+12 ft/sec 

-12 ft/sec 
+12 ft/sec 

-14 ft/sec 
+ 5 ft/sec. 


Mainline Speed Changes 


Vso. Vsf 




30 ft/sec, 
45 ft/sec. 
45 ft/sec, 
60 ft/sec, 
60 ft/sec, 
88 ft/sec. 


45 ft/sec 
30 ft/sec 
60 ft/sec 
45 ft/sec 
88 ft/sec 
60 ft/sec. 


System Entry (Vehicle 
initially stationary) 


V(0) = 0, 


Vs 


30 ft/sec 
45 ft/sec 
60 ft/ sec 
88 ft/ sec. 




Emergency Braking 


V(t), aE 




0-93 ft/sec, 6.43 ft/sec^ 
0-93 ft/sec, 12.86 ft/sec2. 


System Startup 


V(0) = 0, 


Vs 


Same as for System entry. 



-12- 




«o 
o 

t. 
o. 

< 

i. 
o 






u 
to 

i. 

4-» 

3 
O. 
E 
o 



en 



iHi 



The second input, vehicle status information, would be compared with 
the command information so that large deviations in a vehicle's state could 
be detected. It is estimated that up to 90% of the CPU's "active" processing 
time would be focused oVi this task. 

The sector-computer "output," which is shown at the extreme left of 
Fig. 4, consists of an ID number, Vci and Xq-j. These would be encoded and 
communicated to the ith vehicle— a process which would be repeated every T^, 
sees.* A similar signal would also be sent to every other vehicle in the 
sector every Jq seconds. 

In essence, without any further discussion of the architecture shown 
here, all required Xq and Vc trajectories are permanently stored so that "table 
lookup" may be employed together with a limited amount of sector-level processing. 

It should be noted that no provision for redundant operations, and thus 
enhanced reliability, has been made. Clearly, this would be an essential fea- 
ture of any operational unit. 

b) Permanent Memory Requirements 

Next consider the specification of the permanent memory required if 
all individual vehicle position and velocity trajectories were either stored 
for "table lookup" or available with a near-minimum of processing per Fig. 4. 
i) Constant-Speed Operation 

The information required for operation at a specified fixed speed is 
determined via the procedure shown in the following example. 



* Alternatively, the complete trajectory could be transmitted to 
each vehicle before it entered the sector. A vehicle v/ould follow its 
assigned trajectory unless a modification were subsequently transmitted. This 
would be necessary, for example, if an emergency condition were to develop. 



-14- 



Example 1 



Ls = 3280 ft. 



Vs = 30 ft/sec. 



Tj, = 0.1 sec. 



Ts = 3280/30 = 109.3 sees. 
Ns = Ts/0.1 = 1093 words. 
Here Tj is the time required for a vehicle, traveling at 30 ft/sec, to traverse 
a sector, and Ns is the corresponding number of times two-v/ay communications 
between that vehicle and sector control occur. 

The results of computations for the four specified speeds are given 
in Table III, from which it should be noted that the total requirement is 
2742 words. 

ii) Mainline Maneuvering 
A typical moveup trajectory is shown in Fig. 5. In general, the corres- 
ponding maneuver would encompass two of more sectors, and can be initiated or 
terminated at any point within those sectors. Thus, if a strict "lookup" pro- 
cedure were employed, one v/ould store each allowed trajectory for every possible 
(Vs. Xg) combination. As the number of identifiable X's in a sector is Ls/AX = 
65,600, the number of trajectories to be stored would clearly be excessive. 
This number can be reduced by two orders of magnitude via a nominal amount of 
sector-level processing. 

Consider a moveup operation which is to be initiated when a vehicle, 
traveling at a speed Vg, enters a sector. Per Fig. 5, the required speed tra- 
jectory would be 

Vc(t) = Vs + aot <. t < AVy./ao 

Vc(t) = Vs + AV^ AVr/ao < t < Y (2-1) 

Vc(t) = (Vs + AVr) - a^t Y < t < Y + AV^/ao 



-15- 





TABLE III 






INFORMATION REQUIREMENTS— 




CONSTANT-SPEED OPERATION 




Vs 
(ft/sec) 


Ts 
(sees) 


Ns 
(words ) 




30 


109.3 


1093 




45 


72.9 


729 




60 


54.7 


547 




88 


37.3 


373 


E = 2742 words 



where y Is the time the vehicle is to begin decelerating back to mainline speed.* 
The corresponding required position trajectory would be 
Xc(t) = Xs + Vgt + ijaot^ < t < AVr/ao. 



v,(t) 







Fig. 5 Typical moveup velocity trajectory. 



* For convenience, the subscript i (e.g., Vci(t)) is deleted in 
this analysis. 



-16- 



Vs+AV, 



%^^\ 



AV, 



r . 







Time 



(a) 



(b) 




(2-2) 



k,Tc 

(c) (d) 

F1g, 6 Tra jetton' es employed in moveup/moveback maneuvers, 

Xc(t) = Xs + (Vg + AVr)t AVy./ao < t < Y 

Xc(t) = Xg + (Vs + AVp)t - HSi^t^ y < t < Y + AVy./ao 

Here, as the vehicle enters the sector at t = 0, Xg = 0. 

The corresponding discrete versions of these speed and position command 

trajectories are obtained by evaluating (2-1) and (2-2) for t = 0, Tc, 2Tc, 

....etc. The results are as follows: 



Time 


Command Speed 


Command Position 


(K) 


Vc(KTc) 


Xc(KTc) 





Vs 


Xc(0) = 


1 


Vs + aoTc 


Xc(Tc) = Xi 


2 


Vs + ao2Tc 


Xc(2Tc) - X2 



Here, a shorthand notation has been used for the command positions, 



-17- 



K = 1 Xc(Tc) = VsTc + JjaoTc^ A X] 
K = 2 Xc(2Tc) = Vs(2Tc) + HSiQ^Tc'^ £ X2 etc. 
Next consider a case where a vehicle, traveling at a fixed mainline 
speed, is K-; time units "into" a sector. At this time t = KiT^, it is desired 
to initiate the moveup operation specified above (Compare Figs. 6(a) and (b) 
with Figs. 6(c) and (d)). The required speed and position commands could be 
formed from (2-1) and (2-2), and thus the above listing, in the following 
manner: 



Time 


Command Speed 


Command ! 


(K) 









Vs 


Xc(0) = 


1 


Vs . 


Xc(Tc) = V3TC 


2 


h 


Xc(2Tc) = 2VsTc 



Kl 


Vs 


Ki + 1 


Vs + aoTc 


Ki + 2 


Vs + ao2T, 



Xc(KlTc) = K^VsTc 

Xc[(Kl + l)Tc] = KiVjTc + Xi 

Xc[(Kl + 2)Tc] = KiVsTc + X2 



Mote that the same correnand position notation X], X2, .... etc. as previously 
used has been employed here. 

It should be apparant that this type of processing can be employed with 
all moveup/moveback maneuvers, emergency braking, and speed changes. 

A second aspect of such maneuvers is the required maneuvering distance. 
Per Fenton et al^', the total distance required for an n-slot moveup is 

-18- 



D = nHtV,.I!M£.Myi: (2.3, 

AVp do 

where H^ = desired time headway (This would be the time equivalent of 1 slot 

In a synchronous system), and n = number of slots of moveuo. Tii^ ui stance reqjired 

for a moveback maneuver of n slots Is 



D - -nHtV3 . IlMs! . VsAVr 



AVr ao 



(2-4) 



If an Improper value of AVp were selected with a given Vg, the specified 
trapezoidal trajectory would not result. If It were necessary to employ such 
a trajectory, as Is assumed here, one would be restricted In his choice of AVp. 

Consider two moveup trajectories—one of which Is a valid choice and 
a second of which violates the constraint of a trapezoidal trajectory. 
Example 2 ( A 1-slot moveup) 
Condjt2ons_ 

Vg ^ 60 ft/sec; AV^ = 12 ft/sec, and ao = 3.22 ft/sec^. 
Comp£tat2pns_ 

Acceleration phase 

AVp/ao = 12/3.22 = 3.73 sec. 

Words required = 3.73/0.1 = 38 words 

Constant-speed phase 

Moveup speed = 60 + 12 = 72 ft/sec. 

Time to traverse a sector = Ls/(Vs + AVp) = 45.6 sec. 

Words required = 45.6/0.1 = 456 
Deceleration phase 

-AVr/-ao = 3.73 sec. 

Words required = 3.73/0.1 = 38 words. 

-19- 



Total words required 

38 + 456 + 38 = 532 words. 
Next the required moveup distance must be checked. Per Eqn. (2-3), for a 1-slot 
moveup and H^ = 1 sec, 

D = 60 + 3600/12 + 60 X 12/3.22 = 583.6 ft. 
For the specified trajectory, one has the distance traveled during the acce- 
leration phase, the constant- speed phase and the deceleration phase. These 
should, of course, sum to the distance required for a 1-slot moveup. Thus 

D = 2[Vs ^ + »5aoti2] + (Vg + AVr)T 

^0 

or 

583.6 = [2 X 246.2] + 72T. 

Since T = Y - AV^/ag, which is the time spent at speed Vg + AV^, is greater 

than 0, the desired type of trajectory would result. 

Example 3 (A nonpermitted moveup maneuver) 

Conditipns__ 

Vs = 60 ft/sec; AV^ = 14 ft/sec; and ao = 3.22 ft/sec^. 

Computa^tipns_ 

Per Eqn. (2-3) for a 1 slot moveup with H^ = 1 sec, 

D = 60 + 3600/14 + 60 X 14/3.22 = 578 ft. 

This distance as calculated via Eqn. (2-2) is 587.4 + 72T ft. Clearly, 

578 f 587.4 + 72T 

unless T < 0. Thus no time would be spent at the maneuvering speed and a 

trapezoidal trajectory would not result. 

The results of a series of computations are shown in Table IV. It is 

noted that the choices of AV^ employed here were chosen arbitrarily and some 

storage could be saved by employing fewer values of AV^..* The total number of 

words required for those selected is 5346. 

*0ne reasonable choice of online speeds might be 22, 44, 66 and 88 ft/ 
sec. With this choice, perhaps only 1 or 2 AVr's might be employed. 

-20- 



TABLE IV 
INFORMATION REQUIREMENTS- 
ONLINE MANEUVERING 



Vs 
(ft/sec) 


AVp 
(ft/sec) 


Vs + AVr 
(ft/sec) 


tl 
(sec) 


x(ti) 

(ft) 


n 

(ft) 


Words Required 


30 


-7.5 
+7.5 


22.5 
37.5 


2.33 
2.33 


61.2 
78.6 


159.9 
219.9 


1506 
923 


45 


-7.5 
+12.0 


37.5 
57.0 


2.33 
3.73 


96.1 
190.2 


329.8 
381.4 


48 
651 


60 


-12.0 
+12.0 


48.0 
72.0 


3.73 
3.73 


201.42 
246.2 


463.6 
583.6 


759 
532 


88 


-14.0 
+5.0 


76.0 
93.0 


4.35 
2.15 


352.5 
196.6 


848. 
1773. 


530 
397 

T = 5346 



ill) Mainline speed changes 
This is almost a subset of the previous case, and if Vg and AV^ were 
chosen carefully this case would be incorporated into Table IV. However, this 
was not the case here, and Table V was prepared via an analysis of Figs. 4(c) 
and (d). The total number of words required is 362. 

iv) System entry 
In a previous study^^, it was determined that an initially stationary 
off-line vehicle could be satisfactorily merged into a high-speed (88 ft/sec) 
traffic stream with a merging time of 30 sec. With this information, one can 
readily prepare Table VI, wherein it is noted that the required words total 
1200. 

It is important to note that precisely these same trajectories could be 
employed for a startup maneuver (after system shutdown); thus, the latter need 
not be considered separately. 

v) Emergency braking 

Let a vehicle be in the state 

-21- 



Vi(KT) = Ve 

Xi(KT) = Xs 
when it is cotwnanded to emergency brake at a constant rate ae. The corres- 
ponding position command trajectory is 

Xc(t) = Xs + Vet - ^aaet^ (2-5) 

As in the maneuvering case, one can set 

Xs = 
and only store 

Vgt - ^aet2 
which is valid for a specified Vg. It can be applied to a vehicle in the state 
(Vg, Xs >. 0) by adding Xg via simple processing. Thus, a trajectory need only 

TABLE V 
INFORMATION REQUIREMENTS- 
MAINLINE SPEED CHANGES 



Vs(0) 
(ft/sec) 


Vs(tf) 
(ft/sec) 


AVr/ao 
(sec) 


Words 


30 


45 


4.658 


47 


45 


30 
60 


4.658 
4.658 


47 
47 


60 


45 
88 


4.658 
8.696 


47 
87 


88 


60 


8.696 


87 



E = 362 words 

be stored for each possible value of Vg and ag. The possible velocity values 
are specified as 5-93 ft/sec in 0.5 ft/sec steps, and ag as 6.43 ft/sec2 and 
12.86 ft/sec2. The information associated with a given speed and braking rate 
is computed as per Example 4. 

-22- 



TABLE VI 
INFORMATION REQUIREMENTS 
SYSTEM ENTRY (Merging Operations) 



Initial Speed 


Vs 
(ft/sec) 


(sec) 


Words 







30 


30 


300 







45 


II 


300 







60 


n 


300 







88 


II 


300 


Z = 1200 words 



Example 4 

For convenience, braking operations are assumed to begin at t = when 

the vehicle just enters the sector. Let Vg = 88 ft/sec and ag = 12.86 ft/sec^. 

The command velocity is 

Vc(t) = 88 - 12.86t, 

and the vehicle is stopped at a time (ts) such that 

= 88 - 12.86ts 
or 

tg = 88/12.86 = 6.82 sec. 

Ns = 6.82/0.1 = 69 words. 
The results of computations for all permitted speed-braking rate combinations 
are shown in Table VII. The total words required are 20,288— a number which 
is much larger than desired. 

It seems expedient to determine if additional sector-level processing 
could be employed to reduce this number. Rewriting Eqn. (2-5), there results 

Xc(t) - Xg + ^aet2 = Vgt. 

Clearly, the term Jjagt^ is common to all trajectories for a given a^, although 

the total time required is different for each Vg, Thus consider storing both 

Xc(t) - Xj (with Xg = 0) and J^agt^ for the highest speed case. 

-23- 



TABLE VII 
INFORMATION REQUIREMENTS- 
EMERGENCY BRAKING 



V(te)^ 
(ft/sec) 


ae ^ 
(ft/sec2) 


Ns 
(words ) 


0-93 
0-93 


6.43 
12.86 


13488 
6800 



Z = 20,288 words 
The function Vet is a ramp with slope Ve- The longest braking time 
expected is 14.2 sec corresponds to Ve = 93 ft/sec and ae = 6.43 ft/sec^. 
Let tu(t) be stored for 14.2 sec, and consider the following processing se- 
quence for a vehicle in the initial state (Ve» Xg >. 0). 

a) Specify (Ve, Xg >. 0) 

b) Remove u(t) from storage (x is a dunmy time 
variable and u(t) is a unit-step function). 

c) Let T = t - t|<, where t^ is the time the 
vehicle under consideration is to begin 
decelerating. Form (t - t|<)u(t - t^) 

d) Multiply by Ve 

e) Add Xs to Ve(t - tk)[(t - tk)u(t - t^)] 

f) Remove ^ae^^ u(t) from storage 

g) Let T = t - tk to form ^ae(t - tk)2u(t - t|^) 

h) Sum to obtain the desired position corranand signal 
Xc = Xs + Ve(t - tk)u(t - tk) - Jsae(t - tk)2u(t - tk)* 



* An additional processing capability would be added to Fig. 4 if 
these operations were to be performed. 



-24- 





TAB 


LE VIII 






INFORMATION REQUIREMENTS- 




EMERGENCY BRAKING 
(Modified Approach) 


Function 


ae 

(ft/sec2) 


Max Time 
(sec) 


Words req'd. 


tu(t) 


- 


14.2 


142 


Hsiet^ 


6.43 


14.2 


142 


Hsiet^ 


12.86 


7.1 


71 



I = 355 words. 

The permanent word storage associated with this approach is listed in 
Table VIII. Such an approach, if it could be implemented simply with a negli- 
gible amount of online processing, would be extremely attractive as only 355 
words of permanent storage would be required. 

vi) Information Requirements— Summary 

The total word requirement for the case under consideration is sum- 
marized in Table IX. In essence, if the complete braking trajectories were 
stored, the requirement is some 30,000 words whereas if the modified approach 
were used, the requirement would be approximately 10,000 words.* 

TABLE IX 

SUMMARY OF 

INFORMATION STORAGE REQUIREMENTS 



I 



Function 


Words 


Constant Speed 


2742 


Online Maneuvering 


5346 


Mainline Speed Changes 


362 


Merging Operations 


1200 


Emergency Braking 


20,288 


Emergency Braking (modified) 


355 



I = 29.919 words 
T. = 9986 v/ords 



* If 10,000 words were stored, a 14-bit address word would be required 

in Fig. 4. 

-25- 



vii) Estimate of required wordlength 
An estimate of the required word length may be obtained using the 
parameters listed in Table I. In general, each word v/ould be comprised of 
four components corresponding to bits for vehicle identification, position, 
velocity and error detection and/or correction. 

1) Identification Bits 

Ls 3280 «, « . , . 
y-— r = =37.2 veh/sector. 

^Vs)max 88 
As 2^ = 64, 6 ID bits would be required. 

2) Position resolution 

i| = 65,600 

As 2^7 = 131, 072, 17 bits would be required to 
achieve this resolution. 

3) Velocity resolution 

ForAV =0.1 ft/sec and V £ [0, 93] one would require 

2" > 930 
or 10 bits. 

4) Error detection/correction 

It is estimated that 8 bits would be required. 
The estimated word length is thus 6+17+ 10 +8= 41 bits. As this 
would be excessive, especially if an error detecting/correcting code were 
employed to transmit information to each vehicle, one would probably reduce 
this length via the dropping of nonsignificant bits and the elimination of 
redundant information from the command signals. 



-26- 



vli) Approach 1— Summary 

Per the preliminary analysis given here, this approach is clearly a 
feasible one. The primary advantage is that accurate trajectories are stored 
and thus directly available to the CPU. 

The disadvantages are: 

a) The supervision of the sector-level processing 
might tend to be unduly complex. 

b) A large amount of data must be communicated to 
each controlled vehicle. 

c) The probability of errors in the encoding/com- 
munication/decoding process could be higher 
than desired. 

This approach would be more attractive if appropriate coding were 
employed to reduce the data transmission requirements.* 
E. Approach 2 

a) Computer Architecture 

In the second approach, all allowed acceleration trajectories are 
stored in memory. When a given position/velocity trajectory is required, 
the corresponding Aj. trajectory is recalled from memory and processed to pro- 
vide the required V^ and X^, information. The latter is transmitted to a 
controlled vehicle. 

The required computer operations may be accomplished via the archi- 
tecture shown in Fig. 7. Here, as in Approach 1, there would be two general 
inputs to the CPU—one comprising command information for each vehicle in the 



* In the analysis presented, no provision was made for redundancy 
and thus enhanced reliability. Such provision would result in a more complex 
configuration than was considered. 

-27- 




cvi 



u 

o 
1. 
o. 

«c 

&. 
o 



a; 



4) 



u 
le 

i. 



E 
o 



en 



-28- 



sector, and the second, status information pertaining to each vehicle. The 
former would be employed to select an acceleration trajectory for each vehicle, 
which together with that vehicle's ID number, would be the CPU "output." 

The operations required to generate command position and velocity tra- 
jectories for a given vehicle, say Vehicle i, are also shown in Fig. 7. In 
each communication interval, which is of duration T^, an updated acceleration 
command A^ would be processed, via two accumulators, to provide Vc-j and X^.^. 
These signals would be inserted into a multiplexer, which v/ould be synchronized 
via the vehicle ID number, encoded and transmitted to the ith vehicle.* In 
addition, they would be fedback to the CPU for checking purposes. Similar 
operations would be required for every other controlled vehicle; thus, if n] 
were the maximum number of vehicles in a sector, n] registers and 2n"i accumu- 
lators would be required. 

Here, no provision for redundancy and thus enhanced reliability has 
been made. Clearly, this would be an essential part of any operational unit. 

b) Considerations Associated with Acceleration Quantization 

One primary parameter is the acceleration quantization level (AAc) and 
this, together with the time per event Tck» determines both the velocity quan- 
tization level (AVj.) and the position quantization level (AXc). These levels 

are related via 

AVc = AAc TCK 
and 

AXc = ^^Ac TcK^ 
One would like to make both AAc and Tqk very small numbers so as to have 
extremely accurate quantized representations of both Vc(t) and Xc(t). For 
example, if AAc " ^*^ ft/sec^ and Tqk = 0.01 sec. Then 

* An alternative approach involves the generation of the complete 
trajectory, and its transmission to a vehicle prior to that vehicle's entry 
into the sector, 

-29- 



AVc = .001 ft/sec 
and 

AXc = 5 X 10-6 ft. 
With such levels, the quantized functions 9c(t) and X^Ct) would be practically 
the same as their continuous counterparts Vc(t) and Xc(t), and the quantization 
errors would be negligible. The word lengths for these choices are 17 bits for 
velocity and 30 for position (A velocity range of 0-93 ft/sec and a position 
range of 0-3280 ft was assumed here). These lengths are excessively large— 
especially in the context of communicating information, via an error detecting/ 
correcting code to each vehicle. Thus, in practice, it would probably be 
expedient to either round off or truncate the lowest-order bits. Thus, for 
example, if command velocity were to be resolved to within .05 ft, the required 
word lengths could be reduced to 9 and 17 bits respectively. Further reductions 
in the lengths could be obtained by using the redundancy inherent in V^ and 
Xc so that only a significant "critical" part of each word would need to be 
transmitted. 

Clearly, the word lengths could be substantially reduced by increasing 
AAc and TcK. However, if AAc were large (e.g., AA^ >. 4 ft/sec2), a substantial 
corranand jerk would be present when Ac changed. This could result in a jerky 
and uncomfortable ride (The ride quality would, of course, also depend on such 
factors as vehicle controller design and the inherent jerk-limiting properties 
of the vehicle). 

Thus, the choice of quantization levels is, in part, dictated by somewhat 

opposing requirements— a large value of AAc to reduce the required word length 

and facilitate reliable communications versus a small AAc for a comfortable 

ride. 

-30- 



c) Permanent Memory Requirements 

Next consider the amount of permanent memory required 1f all accele- 
ration trajectories are stored for table "lookup." In essence, one must 
have an acceleratlon-versus-tlme profile corresponding to each of the tra- 
jectories specified In Section C. 
1) Constant Speed 

In this case, A^. = for all ti and thus only a single word need be 
stored. It would also be necessary to store the desired stream speed, as this 
would be added as an Initial condition to the "velocity" accumulator output. 
Alternatively, one could store a single word, which would consist of Ac = 
and Vc = constant, for each of the four desired stream speeds. 
11) Online Maneuvering 

Typical maneuvering trajectories are shown In Fig. 6, from which It 

should be noted that the required acceleration trajectory Is a plecewlse- 

constant function. Initially, a vehicle would be In a constant-speed mode 

characterized by 

Ac(t) =0 Vs = Vsi - 

Subsequently, the following three-word command would be applied 

Ac(t) = ao 

Ac(t) = 

Ac(t) = -ao . 

Upon completion of the maneuver, the command would again be 

Ac(t) =0 Vs = Vsl. 

Eight maneuvering situations have been specified (See Table II), and 

thus eight 3-word trajectories would be required. Each word would contain 

Ac(t) and the time It was to be applied. 

-31- 



iii) Mainline Speed Changes 
This case is quite similar to the previous one. Prior to the initiation 
of a mainline speed change, the command would be 

Ac(t) = 0, Vc(t) = Vsi (Constant) 
The subsequent command would involve 

Ac(t) = ao 
for the necessary amount of time followed by operation at the new stream speed 

Ac(t) = 0, Vc(t) = Vs2 (Constant). 
Seven speed-changing situations were defined in Table II; thus, there 
would be a requirement for no more than 7 words. Each word would contain 
Ac(t), and the time interval over which it was to be commanded. 

As the same acceleration values, ag and -ao would be used in both 
maneuvering operations and for mainline speed changes, one could achieve some 
modest word saving by choosing A\V (See Table II) so that some portions of 
the maneuvering and speed-changing trajectories v/ere common, 
iv) System Entry 
In a study of merging operations^', it was specified that the following 
trajectory was one satisfactory choice: 

Ac(t) = 2Ki + 6K2t [0, TJ. 
Here, K] and K2 are determined by constraints imposed at t = Tm, the time at 
which a merging vehicle is inserted into mainstream traffic. 

Both the word size and the number of words required are dependent upon 
the quantization level M^. For example, consider the case where the terminal 
constraints are Vj,(T,t,) = 88 ft/sec, Ac(Tm) = 1.6 ft/sec^ and T^ = 30 sec. For 
these values, 

Ac(t) = 4.264 - 0.088t t e [0. 30]. 
-32- 



This function is shown in Fig. 8, together with quantized functions corres- 
ponding to AAc =0.2 ft/sec2, and 0.8 ft/sec^. Fourteen words are required 
for the former and 3 for the latter. If one makes a conservative choice of 
AAc = 0.2 ft/sec2, some 20 words would be required for the merging operations 
defined in Table II. 

Each of these words would consist of two parts— one to define the 
desired acceleration and a second to define the time that acceleration would 
be applied. As the range of command accelerations is encompassed in -13 to 
8 ft/sec^, 7 "acceleration" bits would be required. It would appear that 9 
"time" bits, corresponding to a maximum time of 51,2 sec, would be sufficient. 
Thus, a 16-bit word could be employed, 
v) Emergency Operations 

As two emergency braking values were selected, one would require only 
two words— provided the words were properly processed and transmitted to a 
vehicle.* 

d) Approach 2--Summary 

A summary of the estimated storage requirements for Approach 2 is 
shown in Table X, from which it should be noted that only 57 words would be 
required. A conservative word size would be 16 bits, if the quantization 
level were selected as 0.2 ft/sec^. 

Per the preliminary analysis presented here, this approach appears 
feasible and includes the following advantages: 

i) The permanent storage requirements are minimal; and 
ii) Extremely accurate trajectories, which can be 

used to obtain estimates of both Vj.(t) and Xc(t), 
can readily be stored. 

* As the time duration of a braking trajectory depenjjs on a vehicle's 
initial speed, this must be considered in the generation of Vc(t) and Xc(t). 

-33- 




(/I 
u 



t 

O 

u 

Oi 



c 
E 



to 

u 
u 

le 
I 

"D 



O 

u 

<•- 
o 

c 
o 






cy 

00 

OS 



< 



-34- 



TABLE X 

SUMMARY OF 
INFORMATION STORAGE REQUIREMENTS 
(Approach II) 



Function 


Trajectories 


Words 


Constant Speed 


4 


4 


Online Maneuvering 


8 


24 


Mainline Speed Changes 


7 


7 


Merging Operations 


4 


20 


Emergency Braking 


2 


2 



Z = 57 words. 

The disadvantages are 

i) A substantial amount of sector-level processing 

is required; 

ii) The probability of an error in either V^ or Xq 

might be increased via this processing; 

iii) A large amount of data (The same as in Approach 

1) must be communicated to each vehicle; and 

iv) The probability of errors (The same as in 

Approach 1) in the encoding/communication/ 

decoding process could be higher than desired. 

This approach would be quite attractive if the probability of a 

sector-level processing error were negligibly small, and if efficient coding 

were employed to reduce the data transmission requirements. 
F. Approach 3 

a) Computer Architecture 

In the third approach, all allowed acceleration trajectories would be 
stored in memory at the sector level and onboard each controlled vehicle. 

-35- 



When a specific position/velocity trajectory v/ere required, the corresponding 
Ac would be recalled from memory, at both the sector level and onboard the 
controlled vehicle, and processed to provide the required X^ and Vc information. 
Thus, this information would be available at both locations. Some redundancy 
is involved here; however, the availability of two independent computations 
of Vc and Xc could be beneficial in terms of system reliability. 

The required sector computer operations could be accomplished via the 
architecture shown in Fig. 9. Here, as in the previous approaches, there 
would be two inputs to the CPU— one comprising command information for each 
vehicle in the sector, and the second status information from each vehicle. 
The former would be employed to select an acceleration for each vehicle, 
which together with that vehicle's ID number, would be the CPU "output." This 
acceleration would be processed, as shown, to provide X^. and Vc for comparison 
with true vehicle position and speed. Mote that the signal transmitted to a 
controlled vehicle would consist of a command selection and an ID number. 

b) Approach 3 — Summary 

The same advantages as associated with Approach 2 are present here; 
in addition, a minimal amount of command information would be transmitted,* 
the probability of errors in the encoding/ communication/decoding process 
would be much less than for Approaches 1 and 2, and Vc and Xc would be avail- 
able in an almost continuous form onboard each controlled vehicle. 

The disadvantages include the following: 

a) A substantial amount of sector-level processing 
would be required; 

b) A substantial amount of processing would be 
required onboard each vehicle; and 

* This matter is considered in detail in Chapter III. 

-36- 




CO 



u 

o 

i. 
a. 

ex. 
< 

o 



a: 

U 



L. 

+J 

3 
O. 
E 
O 

o 






fl 



-37- 



c) The probability of an error in either V^ or 
Xc could be substantial. 
As two estimates of both Xc and Vc would be available, the latter problem 
should be resolvable. 
G. Conclusions 

Three general approaches to sector-level computer operations have been 
examined, and their advantages and disadvantages enumerated. This was done 
primarily to provide a source document for further research efforts, and does 
not, at least at this time, particularily emphasize any given approach. In 
essence, all three appproaches offer particular advantages, and each Is 
worthy of more detailed Investigation. 

It should be noted that a number of other approaches may be formulated 
by utilizing various aspects of the three presented. Ideally, one would like 
to obtain the most beneficial aspects of each and eliminate some of the 
unwanted aspects. The "cost" involved would probably be Increased complexity. 



-38- 



CHAPTER III 
ON SECTOR-LEVEL COMMUNICATIONS 



A. Introduction 

Relatively little effort has been devoted to studying the communication 
aspects of Individual-vehicle, automated ground transport. However, much rele- 
vant work, which was focused on other applications, has been accomplished as 
may be noted In a recent state-of-the-art survey.^® In particular, some useful 
experimental results, which were obtained In a hlqh-speed rail context, are 
available/'-^^ 

The work reported here is a continuation of an earlier effort, ^^ and it 
is focused on communications between a sector-level computer and the individual 
vehicles under its supervision and/or control. The emphasis is on Approach 3 
(which is defined in Fig. 9), as this approach should result in a minimal or 
near-minimal amount of transmitted information. 

B. Minimal Required Information Transmission Rates 

Consider the sector-level structure shown in Fig, 2, and note that the 
computer is the source of command information (Xc(t), Vc(t) and Ac(t)) and the 
controlled vehicle(s) is a source of status information (X(t), V(t), A(t) 
and other data). The information content of these sources is largely dependent 
on the operating policies of a particular sector realization, and 1s thus 
strongly Influenced by technical and economic constraints and safety considera- 
tions. For communication-analysis purposes, the policy adopted may be described 
by an "a priori probability structure." One reasonable structure, which is not 
unique, is defined by the following assumptions: 

-39- 



1) All possible command trajectories would be pre- 
determined, and their number would be manageably 
small. 

2) Each vehicle would be assigned a trajectory prior 
to entering the sector, and each normative trajec- 
tory is equally likely to be assigned. 

3) Each vehicle would be assigned an identification 
number (ID), and the possible assignments would be 
equally likely. 

4) Every T^ sec each vehicle in the sector would 
receive an indication as to whether or not emer- 
gency operations should be initiated. 

5) Under normative conditions, the vehicle/controller 
dynamics would be known (e.g., the dynamics speci- 
fied in Chapter V), and thus a vehicle's response 
to (Xc(t), Vc(t), Ac(t)) would also be known. 

6) The status information would be quantized and the 
probability density functions (p.d.f.) for both 
X(t) and V(t) are knov/n, discrete and uniform for 
all normative conditions.* 

7) A(t) and some other status variables (e.g., oil 
pressure and water temperature) would be quantized 
into tv/o levels — one indicating normal operation 
and the other a failure. 

*The uncertainty in X(t) and V(t) as caused by random disturbances, 
measurement errors, parameter variations, etc. is described in terms of these 
p.d.f. 's. In normal situations, X(t) and V(t) would be the outputs of a low- 
pass system, and thus would be approximately normally distributed over some 
range. However, the use of a uniform distribution is convenient, and results 
in a conservative estimate of source information content, 

-40- 



8) The probability of a failure occurring within a 
given time interval is \/ery small {« 1 failure/ 
10 hrs). 
In three of these assumptions, equally likely (or a uniform p.d.f.) 
conditions are assumed. Since this condition results in a maximum source 
entropy (maximum average information content), the resulting information rates 
would be greater than the minimum values. . 

Consider the calculation of the source entropies for a sector in which 
the traffic flow is saturated (a vi/orst-case communication condition). The 
average information {Iq]) sent from the sector computer, in an H/V time 
interval, to a vehicle prior to its entering the sector would be 

^cl = -Pnor ^092 !"£! - Pem^ "^^^2 ^em^ " Pem2 1092 ^emg" ^^^2 ^ (bits). 

p 
Since P£L is the probability of occurrence of each normative command, the first 

I p p 

term, which is comprised of N_ identical terms (i.e., - nor log, J]£L) » corres- 

ponds to the source entropy associated with commands for normal operation. The 

second and third terms are associated with emergency operation, and since ^J- is the 

V 

probability of each ID assignment, the fourth term is associated with ID selection. 
(All symbols employed in this analysis are defined in Table XI). The average 
information (1^2) sent in an interval ^ to each vehicle already in the 
sector would be 



N 



^c2 = -^nor lo^Z ^nor " ^em^ ^0^2 Pem^ " Pem2 ^^^2 Pem2 (bits). 
Thus, a minimal average information rate (C^) for the command link is 

C = llinL 1,1 + !!v I (bits/sec), 
c H ^' Tc " 

The condition that P^^ <« P^or ^"^ ^em^ ^^^ ^or ^''^'* ^or " ^^ "^^^^^ ^^^^ ^^- 
hicles receive no information while in tiie sector. This is reasonable since Subchannel 
2 is included for safety purposes (i.e., to transmit an emergency signal and the 

-41- 



need for this has a probability close to 0). Gnder this condition 1^2 ^ 

(3-1) 



and 



V 



sm 



Cc = —[1092 Nt + 1092 '^vl- 



A similar analysis may be conducted to obtain a minimal average 

TABLE XI 
DEFINITION OF SYMBOLS 



Symbol 


Definition 


Typical Value* 


Ls 


Sector length 


3520 ft 


Vsm 


Maximum stream speed 


88 ft/sec 


Tc 


Frame time interval (i.e., the interval in 
which each vehicle is addressed once) 


0.1 sec 


H 


Slot size 


88 ft 


Nv 


Maximum permitted number of vehicles in the 
sector 


40 ft 


Nj 


Number of permitted normative trajectories 


16 


Pern- 


Probability that an emergency occurs within 
a given T^ interval and en^r-^fincy comi-and 

i (i = 1, Z) is select.-^:! 


= 


Pnor 


Probability that normal sector operation is 
continued within a given T^ interval (Ppor 
= 1 - Pem) 


= 1 


Csn 


Average information rate as transmitted from 
a "normal" vehicle 


- 


Csf 


Average information rate as transmitted from 
a "failed" vehicle 


- 


Pn 


Probability of normal vehicle operation at 
time t 


- 


Pf 


Probability of a vehicle failure at time t 


- 


•^v 


The range of possible speeds at time t 


4 ft/sec 


^x 


The range of possible positions at time t 


2 ft 



* These values are specified for illustrative purposes only. 

-42- 



TABLE XI(Cont.) 



Symbol 


Definition 








Typical Value* 


qy 


Velocity quantization level 








0.5 ft/sec 


qx 


Position quantization level 








0.5 ft 


By 


Effective power spectrum bandwidth 
random velocity deviations 


of 


the 


2.5 Hz 


Bx 


Effective power spectrum bandwidth 
random position deviations 


of 


the 


1.0 Hz 


ad 


Component of vehicle acceleration 
a disturbance force 


due 


to 


- 


x(t) 


An estimate of X(t) 








- 


v(t) 


An estimate of V(t) 








- 


TAc 


The range of possible A^ 








-20 ft/sec^ to 
10 ft/sec2 


^Vc 


The range of possible Vc 








0-100 ft/sec 


^Ac 


Quantization step-size of I\q 








2 ft/sec2 


^Vc 


Quantization step-size of Vc(= 


=qAc 


Tc) 




0.2 ft/sec 


^Xc 


Quantization step-size of Xc(= 


=%qAc 


Tc^) 


0.01 ft 


e 


Allowance for overshoot 








2 ft/sec 



information rate (Cs) for the status link with the following result: 

Cs = ^ (Pn 1og2 Pp + Pf log2 Pf) + N^CPp Cgn + Pf Cgf). 
'c 
The quantity Cgf is difficult to specify since the state (X(t), V(t)) of a 

failed vehicle is probably a nonlinear, nonstationary process; however, since 

one would expect Pp >» Pf» then 

Cs = Ny Csn* 

Csn is largely determined by the distributions of X and V* (See Fig. 10). 



* Hereafter, X and V will represent estimates of X and V. 

-43- 



These distributions are not statistically independent since X and V are 
linearly related; however, since X and V would be quantized independently, 
and possibly contaminated by independent sources of measurement noise, the 
correlation between X and V would be less than one. For simplicity, X and V 
are assumed to be statistically independent; thus, the resulting calculated 
Csn would be an upper bound on the true value. 



p(x) ., 
or 
p(v) 



■ff 



^v [*- 



'V 

or 
ry 



Impulses of vy/eight 



qx 



1+ qv 



v(t) or x(t) 
(t fixed ) 



Fin. 10. A typical probability density function. 



Note: The mean of this distribution is the deterministic 
response to Xc(t), and would not in general, equal 
XcCt). 



The entropies of the other status variables (e.g., acceleration and 
engine temperature) also affect Csn; however, their effect is negligibly 
small as a result of Assumptions 7 and Q. 

-44- 



Using an approach specified by Schwartz, ^^ 



^v 



'"X' 



Csn = By 1092 (^ + ~) + ^x ^092 (1 + r^) (bits/sec). 



(3-2) 



The quantities By and B^, which are defined in Table XI, could be approximated 

from the frequency-response characteristics of the vehicle's longitudinal 

control system.* 

An indication of the magnitudes of both Cc and Csn "lay be obtained using 

Eqns. (3-1) and (3-2) and the parameter values given in Table X. The result 

is 

C^ = 10 bits/sec 

Cs = 400 bits/sec. 



and 



These values are rather small and are a reflection of the rates required if 
it were possible to transmit all source information in the most efficient manner. 
In practice, one would have much higher rates because of coding constraints, 
safety requirements, and a need for the detection and/or correction of errors 
in transmitted signals. 

This analysis is based on one set of assumptions regarding sector opera- 
tion, and is, of course, not unique in that another set could have been employed. 
However, in general, it appears that the utilization of a "reasonable" set 
would result in the elimination of considerable redundancy from the transmitted 
information and minimal bit-rates. 



* A conservative selection of By and B^ would be the 20db below-peak 

frequency response of JL (jw) and JL (jw), respectively. Here aci(jw) is 

ad 3d 
that component of acceleration due to a disturbance force. 

-45- 



n 



C. Encoding of the Command and Status Information 

Both the command and status information must be encoded* for trans- 
mission, and the requirements of this process result in larger bit-rates than 
the minimal ones specified in the previous section. In that section, the 
word bit refers to a measure of information content, or entropy. Hereafter, 
it will be synonymous with "binit, or binary digit." 

a) Command Link 

This link would consist of two subchannels. Identification and command 
information would be transmitted, on Subchannel 1, to a vehicle prior to its 
entering the sector, and command information would be transmitted on Subchannel 
2 to each of the vehicles already in the sector. The latter information would 
include an indication as to whether emergency operation should be initiated and 
lateral guidance information (It should be noted that the latter was not included 

in the analysis of the previous section). 

An 11 -bit code word is formulated for Subchannel 1 in Table XII 

and, as a vehicle would enter the sector ewery second (for H/V^^.^ =1 sec) 
under saturated flow conditions, the minimal required bit-rate v/ould be 

n bits/sec. 

A 3-bit code word is formulated for Subchannel 2 in Table XIII. Since 

the sector computer would communicate with a maximum of 40 vehicles within 

each Tc = .1 sec, the corresponding bit-rate would be 1200 bits/sec. Thus, 

the total bit rate for the command link would be 1211 bits/sec. 

b) Status Link 

Before specifying the status link bit-rate, the emergency detection 
mechanisms should be defined. Here, it is assumed that an emergency could be 
detected in any of the following ways: 



* Here, only binary, or 2-symbol , communication is discussed. Using 
more than 2 symbols could result in better performance; however, more complex 
transceivers would be required. 

-46- 



TABLE Xr 
FORMULATION OF MINIMAL CODE WORD 
FOR 
SUBCHANNEL 1 



Source 


Information 


Number of bits 


Vehicle ID No. 
Command Selection 


1 of 40 different numbers 
1 of 18 different commands 


6 
5 




E = 11 bits/v/ord 



Source 



TABLE XIII 
FORMULATION OF MINIM;\L CODE WORD 
FOR 
SUBCHANNEL 2 (1) 

Information 



Number of bits 



Longitudinal Command 



Lateral Command (2) 



1. Maintain normal trajectory 

2. Brake at -0.2g 

3. Brake at -0.4g 

1. Guide left 

2. Guide right 



1 



Z = 3 bits/word 



Note: (1) Here the veiiicle ID Mo. is not considered as part of the 
information v/ord; hc-vever, it may be necessary to include 
it for communication and system syncrironization. 

(2) The number of bits required for lateral command information 
is dependent upon the means employed for realizing lateral 
control. For some choices, a third command "maintain present 
course" would be required and thus 2 bits would be needed. 

i) The sector computer processes X(t) and V(t), as 
received from each vehicle, and determines if 
either the oosition or velocity deviations ex- 
ceed decision thresholds (e.g., ± 1.5 ft for 
position and ± 2.5 ft/sec for velocity). 



-47- 



ii) Several types of failures would be detected onboard 
a vehicle, and the corresponding information (1 or 
2 bits) is communicated to the sector computer, 
iii) If A(t), as measured onboard a vehicle, exceeds 
threshold bounds (e.g. |0.2g|),* an emergency 
"flag" is set in the status word. 
The last condition is especially important as it eliminates the need to trans- 
mit A(t). It is not necessary to transmit higher-order bits of position 
and velocity as is illustrated in the following example. 

Consider the velocity-versus-time plot shown in Fig. 11. Here Vc = 
88 ft/sec and the decision threshold is specified as ±2.5 ft/sec. At t = 
(Ki - l)Tc, it is assumed that an emergency isn't detected; therefore 

85.5 < V[(Ki - l)Tc] < 90.5 (ft/sec). 
If the acceleration thresholds (± 0.2g) are not surpassed in the next Tq sec, 

then 

84.86 < V(KiTc) < 91.15 (ft/sec) 

as is shown in the figure. 

If py = 0.5 ft/sec, then it would be necessary to transmit only the 
low order 4 bits of the total velocity word, since each quantization level 
with the interval [84.86, 91.15] could be uniquely identified by these 4 bits. 
A similar analysis may be conducted for the position variable. 

These ideas have been used in the construction of the status word and, 
as is shown in Table XIV; a 9-bit word results. Since each of a maximum of 
40 vehicles comnunicates with the sector computer every 0.1 sec, the minimal 
required bit-rate would be 3600 bits/sec. 



* This criterion would not be employed in system entry operations 
where |a| > 0.2g. 

-48- 



92.0 - 



90.0-- 



Vc=88.0+ 



86.0-- 



emergency 
region 




normal 
region 




t (sec) 



Fig. n The worst-case failure If the 
acceleration bounds are not 
exceeded. 



.49- 



Note that the practical bit-rates for both links are much larger than 
the corresponding information rates given in Section B. Much of this difference 
is attributed to the safety specification that the sector computer must commu- 
nicate with each vehicle at least once in each Tc interval, 

c) Encoding for Approaches 1 and 2 

It is worthwhile to compare the above results with those obtained when 
both the command information (Xc» Vc and Ac) and the status information are 
not transmitted in reduced form (e.g., as in Approaches 1 and 2), In this 
comparison, the parameters specified in Table XI are employed. The step-sizes 
q„ , q and qx^. specified there were chosen to eliminate the effects of 
command quantization noise. (Since this was the case for Approach 3, it seems 
reasonable to make it so here for purposes of a fair comparison). 



TABLE XIV 
FORMULATION OF MINIMAL CODE WORD 
FOR 
STATUS CHANNEL 



Source 


Information 


Number of bits 


Position 


1 of 8 levels (4 ft quantized 
into 0.5 ft increments) 


3 


Velocity 


1 of 16 levels (8 ft/sec quan- 
tized into 0.5 ft/sec increments) 


4 


Acceleration and 
other status 
information 


1. Continuing normal operation 

2. Pending failure 

3. Loss of power 






4. Acceleration bounds exceeded 


2 



1=9 bits/word 

Note: Here the Vehicle ID No. is not considered as part of the information 
word; however, it may be necessary to include it for communication 
system synchronization. 

-50- 



The bit-rate for Subchannel 1 of the command link v/ould be 6 bits/sec 
as the required word would only contain vehicle identification information. 
The minimal required word length for Subchannel 2 is 33 bits as is shown in 
Table XV. Since commands must be transmitted to a maximum of 40 vehicles 
within each 0.1 sec interval, the required bit-rate would be 13,200 bits/sec. 

The word length for the status link is 23 bits as is shown in Table 
XVI, and since the sector computer must receive conmands from a maximum of 
40 vehicles within each 0.1 sec, the corresponding bit-rate is 9200 bits/sec. 

The total required bit-rate is some 23,000 bits/sec as compared to 5000 
bits/sec for Aoproach 3.* Clearly, the channel bandwidths may be significantly 
reduced by effectively utilizing a priori knowledge. 






TABLE XV 
FORMULATION OF NOMINAL CODE WORD 
FOR 
SUBCHANNEL 2 



Source 


Information 


Numb 


Br 


of bits 


Xc 


1 of (1 + ^s ) levels 
qXc 






19 


Vc 


1 of (1 + ''^^) levels 
nVc 






9 


Ac 


1 of (1 + ''^^) levels 






4 


Lateral Guidance 


1. Guide left 










2. Guide right 


Z= 




1 




33 bits. 



* Note that additional bits may be necessary for synchronization and 
error-detection and/or correction. 



-51- 





TABLE XVI 




FORMULATION OF NOMINAL CODE WORD 




FOR 




STATUS LINK 




Source Information 


Number of bits 


X 


1 of (1 + "-s ) levels 
^Xc 


13 


V 


1 of (1 + ''^c + ^) levels 


8 


Acceleration and 
other status 
information 


(Same as before) 


2 



I = 23 bits/word. 

D. Coding for Error-Detection and -Correction 

Parity bits may be added to an information word for the detection and/or 
correction of errors due to channel noise. Various types of codes have been 
developed for this purpose; here, only the cyclic block codes will be discussed 
because, as a class, these appear to be the most powerful, well -developed and 
easily implemented choice.* 

First, consider the random-error-correctinq capabilities of these codes 
as a function of the number of parity bits. The following assumptions, which 
appear realistic, are made to simplify this comparison: 

1. The number of information bits transmitted per 
unit time is fixed; 

2. There are k information bits per word (Here, 

k = 9, corresponding to the status word derived 
in Section C). 



* A detailed exposition of this class is contained in Peterson and 
Wei don. 2 3 

** A random-bit error is one which occurs independently of all other 
errors. .52- 



3. The binary symbols are equiprobable and have 
equal energy. 

4. The channel noise is additive (no fading), 
normally distributed and white. 

5. The signals are detected via noncoherent, 
frequency-shift keying, 

6. The average received signal power is fixed 
(i.e., it is independent of bit frequency). 

In view of Assumptions 1, 2 and 6, the addition of parity bits would 
result in a decrease in the energy per bit. Thus prior to decoding, the pro- 
bability of an error occurring within a code word would be increased by two 
mechanisms — the bit- error probability would be increased due to a decrease 
in signal-to-noise ratio, and the number of bits per v/ord would be increased. 
However, after the decoding process, the word error probability would usually 
be less than it would be if no parity bits are used. 

The random-error-correcting properties of several (n, k) codes, which 
are among the most powerful known for this purpose, are compared in Table XVII. 
Here, the following symbols are employed: 

n = the total number of bits per word; 
do* = the BCH bound^^ on the minimum Hamming distance; 
F = the average signal energy per bit; 
Nq = the power spectral density of the noise; 
Pe = the probability of a bit error (P^ = ^e ^^) 

Pq = the probability of obtaining the correct code word 
after decoding. 

* If a (BCH) code is characterized by d^, then it can correct all com- 
binations of to or fewer errors, where do = 2to + 1. 

** The equation is valid for noncoherent detection of a frequency-shift 
keyed signal in a non-fading channel. 

-53- 



TABLE XVII 
COMPARISON OF SEVERAL RANDOM-ERROR CORRECTING CODES 



(n. k) do 4r- (dB) 



1 - Pr (approximate upper bound) 



(9. 9) 





14.2 


1.0 X 10-6 


9 X 10-6 


(15. 9) 


4 


12.0 


1.9 X 10-4 


3.8 X 10-^ 


(21, 9) 


6 


10.5 


1.8 X 10-3 


7.5 X 10-6 


(31. 9) 


12 


8.8 


1.1 X 10-2 


1.0 X 10-6 



Note that P^ is only moderately improved if oarity bits are used. Further, 
as the decoding process would require a special-purpose computer. ^^ the use 
of these codes may not be feasible. 

A more effective means of reducing 1 - Pq would be to increase E/Nq. 
For example, if no parity bits were employed and Eq/Nq = 20db. then 1 - Pq = 
10-21, This would, of course, correspond to the virtual elimination of random 
errors . 

In practice, spurious, nonstationary and sustained disturbances, or 
burst noise, would tend to cause groups of bit errors (burst errors).* In 
these cases, increasing E/Nq may not be adequate since the instantaneous 
noise power could be unpredictably large. Mere, codes designed for error- 
detection and burst-error-correction could substantially improve communication 
system performance. 

Let t^. the time required to transmit one code word, be fixed (i.e.. 
it is independent of n). All burst errors of length b. which would be due to 
noise bursts of duration -JL , would require at least 2b parity bits for 



* A burst error of length b is a sequence of b bits of which at least 
the first and last are in error. 

-54- 



correction. Several superior burst-error- correcting codes are shown in Table 
XVIII. For example, a (15, 9) code could correct one error less than or equal 
to 3 in length in a single code word. 

Noise bursts of duration greater than — - would result in uncorrectable 
burst errors; however, all burst errors of up to duration (n - k) and most of 
those greater than (n - k), would be detectable.* For example, one well - 
designed (15, 9) code would detect all errors of length less than or equal to 
6, 96.8% of all burst errors of length 7, and 98.4% of those of length 8 or 
greater. Thus, in most practical cases, the probability of an undetected 
error could be made negligible. In practice, the duration of noise bursts 
would, at times, probably exceed tw/2; hence, to avoid false corrections, cyc- 
lic codes should be used for error detection only. 

The decoding circuits associated with error detection and burst error 
correction, unlike those for random error correction, are simple and inexpen- 
sive. Some typical circuits can be found in Peterson and Wei don. ^^ 

TABLE XVIII 
THE PERFORMANCE OF SOME BURST-ERROR CORRECTING CODES 



(n, k) 


Burst- 

Abi 


■Correcting 
lity b 


b 
n 


(15, 9) 




3 


.20 


(19, 9) 




5 


.26 


(21, 9) 




6 


.29 


(25, 9) 




8 


.32 



Note: — < 0.5, and the upper bound may be approached only by 
choosing n - k large. 

* Any cyclic code with n - k parity bits could detect a burst error of 
length n - k or less; also the fraction of bursts of length b > n - k that 

could be undetected is 2"^" " "^ ' ^) for b = n - k + 1 , and 2-(" " •^) for b > n 
- k + 1. Thus, the only burst errors that could be undetected are those which 
transform one code word into another. 

-55- 



E. S ynchronization 

Synchronization between transmitter and receiver is essential to the 
operation of a clocked communication system. In the application of interest 
here, one channel could be shared by many separate transmitters and receivers 
through time-division multiplexing and the loss of synchronization could have 
serious consequences. For example, if the transceiver in one vehicle were 
out of synchronization with the system, it could interfere with communications 
between the other vehicles and the sector computer. 

Synchronization is also important for control purposes as it provides 
the time reference for the vehicles' trajectories. A value for X^, however 
precise, has little meaning If the corresponding time, at which it is appli- 
cable, is not known. Thus, a reliable time reference is as necessary as a 
reliable position reference. 

The following synchronization levels are listed in order of decreasing 
time ambiguity: 

1. Carrier synchronization (This would be required 
if coherent detection methods were employed); 

2. Bit synchronization to mark the beginning of 
each bit. 

3. Word synchronization to denote the beginning of 
each code word. 

4. Frame synchronization to define the time interval 
{1q) in which all vehicles were addressed at 
least once. 

Theoretically, each of the lower synchronization levels (1 - 3) could be 

derived from a higher one. However, in practice, it is easier to achieve and 

and maintain total synchronization by using separate methods for some or all 

of the lower levels. 

-56- 



The following methods have been discussed in detail by Stiffler:^** 

1. The use of separate time and/or frequency channels 
(synchronization at any of the levels listed 
could be achieved In this manner); 

2. The application of maximum- likelihood techniques 
on the information portion of the signal to 
achieve carrier and bit synchronization; and 

3. Special coding methods (prefix, comma, and 
comma-free methods) to achieve word and frame 
synchronization. 

Since the achieving of synchronization is especially critical in a vehicle- 
control application, some combination of these methods would probably be 
employed in practice. 
F. Conclusions 

If the a priori probability structure, which was described in Section 
B, were acceptable, then the required channel capacity would be some 5,000 to 
10,000 bits/sec depending upon the number of parity bits employed. 

Also, a large signal-to-noise ratio should be a primary design goal, as 
— > 20 dB could result in a virtual elimination of random errors. 

Burst errors could be effectively detected and/or corrected via the use 
of a cyclic block code. Ultimately, it may be more practical to simply detect 
errors and not correct them. 

Finally, the Importance of synchronization In sector communications and 
control should not be underestimated— particularly in the application of interest 
here. 



-57- 



CHAPTER IV 
INFORMATION SOURCES FOR LONGITUDINAL CONTROL 



A. Introduction 

There are two types of information sources for vehicle longitudinal con- 
trol shown in Fig. 2— one to provide state information to each controlled 
vehicle, and a second to provide such information directly to the sector computer. 
Hereafter, these sources are defined as Information Source 1 and Information 
Source 2, respectively. 

The following general requirements should be satisfied by both types of 
sources: 

i) The signal available at the receiver (either 
onboard each vehicle or at the sector computer) 
should have a large signal-to-noise ratio; 
ii) This signal should be available in an unambi- 
guous form over the expected range of state 
deviations— both in the lateral and longitudinal 
directions; 
iii) The signal characteristics should be essentially 

unaffected by the environment; and 
iv) The source must be highly reliable so that the 
probability of a failure is extremely low. 
In addition, it was considered highly desirable to obtain highly accurate mea- 
sures of vehicle position (< 0.2 ft error) and "instantaneous" velocity (+1.0 ft/sec 
so that precise control could be achieved under small time-headway conditions. 

-58- 



B. Information Source 1 

The primary purpose of an Information Source 1 configuration is to pro- 
vide sufficient information so that satisfactory individual vehicle control 
can be achieved in both normative and emergency situations. To achieve this, 
it would be desirable to have the following quantities available: 
i) Xc, X and/or Xc - X = AX; 
ii) Vc, V and/or Vc - V = AV; and 
iii) Ac, A and/or A^ - A^ = AA. 
Each vehicle would receive its command state from the sector computer, and it's 
actual state (X, V and A) from the information source. However, there is 
presently no efficient, accurate and economical approach for determining A— at 
least from information received from a roadway-based reference. Therefore, 
the configurations to be discussed will not involve the acquisition of this 
quantity.* 

During a previous study ,^^ three roadway-based configurations v/ere sug- 
gested for use as (or in conjunction with) an Information Source 1. The results 
of detailed experimental studies of each of these are discussed here. 

C. Information Source 1— A Crossed-Wire Approach 

One approach to the measurement of vehicle position is shown in Fig. 
12. Here, widely spaced position-reference markers, hereafter referred to as 
absolute position markers, would be employed to provide an accurate measure of 
a vehicle's absolute position when that vehicle passed over a given marker. 
This would be achieved by employing the detected signal to zero a vehicle-borne 
counter. Intermediate position markers would be located between the absolute 



* This does not preclude the onboard measurement of A, and its use as 
a control /feedback variable. 

-59- 











o 

II ^ 
ct 

o 
p 

o 

o o> 

^ O m 

o £5^ 
\|S| 

O £ C CO 

3.2 ^ 


















Q) 












I. 
3 
O 










■mat Ion 
on. 








«• ^ ^ ^ ^ _ ^„ ^ .^, 


infor 
'polati 










enent, 
inter 


Dsition 


\ 

\ 

9 


— 


discrete el 
Ith position 


GL 






c 

• MM 




• 

CT, 
•r- 


l'5 
o 


J5! 
o 

'1 


3 
O 

o 






I) 


O C 


i C 


:> 





-60- 



markers, and the vehicle counter would be advanced as it passed each such 
marker. The distance traversed between each marker pair could readily be 
estimated; thus, a continuous estimate of X v/ould be available. 

It was previously noted^^ that magnets could be successfully employed 
for absolute position markers because of their high reliability, good reported 
position resolution (within ±1 in), insensitivity to environmental factors, and 
low-noise properties. The use of current-carrying wires for intermediate posi- 
tion markers would result in both these and the following advantages: 
i) Superior position resolution (within ±1/16 in); 
ii) Multiple-frequency excitation for coding purposes; 

and 
iii) Dual use as an information source and a communi- 
cation channel, 
a) A Crossed-Wire Configuration — Theory 

Consider the spatially periodic, wire configuration shown in Fig. 13.* 
Note that the magnetic flux, which results from current flowing in this wire, 
reverses direction each half period (i.e., for each 1 ft of longitudinal travel), 
It is relatively simple to sense this reversal and thereby determine the posi- 
tion of each lateral wire. 

A sensor configuration, which has been used successfully, consists of 
two vehicle-borne, vertically mounted coils spaced 6 in apart, as is shown in 
Fig. 14. The leading coil is used to sense the phase of the field relative to 
the phase sensed by the reference coil. 



* This configuration has been imbedded in a 2209-ft section of asphalt 
berm strip adjacent to the FHWA Skid Calibration Pad at the Transportation 
Research Center of Ohio as is described in Appendix A. 

-61- 




Section A— A 



Lateral 
conductors 



Mognetic 
flux lines 



Fig. 13 Top view of a spatially periodic wire confinuration. 



Vehicle-mounted coils 



^ Vehicle motion 




Roadway 
surface 



Laterally positioned wires 



Tin. 14 The relationship of two vertically nounted, sens inn 
coils to the laterally positioned wires. 



-62- 



Assume that at a given Instant, both coils are between two laterally 
positioned wires. The fluxes linking these coils would therefore be in phase. 
As the lead coil approaches and passes a wire, the flux linking this coil 
would decrease in magnitude, go to zero over the wire, and then increase in 
magnitude but with a phase opposite to that linking the reference coil. 

The signal processing required is achieved as shown in the block diagram 

of Fig. 15. The voltages induced in the sensing coils are amplified, filtered 

to attenuate undesired frequency components, and multiplied. When the two 

voltages are in phase, the multiplier output is 

(A cos wt)(B cos wt) = — [cos 2wt + 1] 

2 

The cos 2wt term is attenuated by the lov/-pass filter following the multiplier 
leaving the constant +AB/2 and additive ripple at 2w rad/sec. 




Phase -reverse I 
sensing coil 



Sref 




Reference coil 



Filter 



Filter 



^flTl 



Sref 



Phase 
Detector 

(Multiplier) 



Low- 
Pass 

Filter 



Fig. 15 A block diagram of the signal processing 
employed with the "crossed-wire" approach. 



-63- 



Threshoid 
Ckt. 



When the phase of the voltage in the lead coil reverses relative to 
that of the reference, the multiplier output becomes 

[A cos (wt + 180°)][B cos (ut] = - ^cos 2a)t + 1]. 

In this case, the output of the low-pass filter is -AB/2 with additive ripple 
at frequency 2(jj rad/sec. 

Thus, when the phase-reversal sensing coil crosses a lateral wire, 
the low-pass filter output changes from a positive to a negative polarity. 
The threshold circuit responds to the zero crossing of this change by changing 
its binary state (This advances a vehicle-borne counter per Fig. 12). 

Since the spacing between lateral wires is twice that between the two 
sensing coils, the reference coil crosses the lateral wire when the phase- 
reversal sensing coil is midway between wire crossings, causing the sensor 
voltages to be in phase once again. The response of the threshold circuit 
to the resulting negative-to-positive transition of its input is ignored by 
all suceeding circuitry. 

In this discussion, relative motion effects in the field-sensing process 
were ignored; however, the motion of the sensor relative to the magnetic field 
induces a component of voltage in the phase-sensing coil which can degrade 
the accuracy of the sensor. 

The voltage (e) induced in a coil of N turns is 

e = N Jdi (volts) (4-1) 

dt 

where cf) = flux linking the coil in webers. This flux distribution may be 

modeled by 

(jj = F(x. y, z)I (4-2) 

where I = current in amperes, and F(x, y, z) is a function uniquely determined 

-64- 



II 



by the geometry of the current-carrying wire configuration, and x, y, and z 
are the coordinates of the sensing point relative to an origin of coordinates 
located as shown in Fig. 14. Because of the complexity of the configuration 
employed, it is simpler to determine F experimentally rather than analytically. 
Upon substituting (4-2) into (4-1), there results 



Mrr/w ,\ <^I ^ T 9P dx ^ - aF dy ^ . 8F dz n 
e = N[F(x, y. z) ^^ I -^+ I ~^+ I -^ ] 



(4-3) 



The last two terms (i.e., the voltage components due to lateral velocity and 
vertical velocity) can be neglected since both 3F/3y and 3F/8z are very small 
over practical ranges of y and 2; therefore, only the first two terms need be 
considered. 

Based on empirical measurements with z = 0.34 ft, y = and N = 400, 
F(x, 0, 0.34) was as observed to be as shown in Fig. 16. This function is 
characterized by a substantial peak magnitude and a nonnegligible rate of 
change with respect to x. Thus, the first term in (4-3), which is the voltage 
Induced due to the time-changing current in the wire. Is not negligible pro- 
vided the current frequency is sufficiently high. It is this term which varies 
in magnitude and phase in accordance with the earlier discussion and should 
therefore be considered as the desired voltage component. 

The second term in (4-3) is due to the longitudinal velocity of the 
vehicle, and it is proportional to both V and 3F/9x. Note from Fig. 16 that 
the derivative, in the region of a wire crossing, is constant and 

1 9F/8X.|^.p^ crossing = ^-^^ x 10'^ weber/amp/ft. 



-65- 



. F(x,0,0.34) weber/amp 



amp/ft 




Fig. 16 An empirically determined choice 
for F(x, 0, .34). 



If the current were specified as 

I = Im sin ojt, 
then, in the vicinity of a crossed wire (located at x = for convenience), 
the voltage (e^) induced in the phase-reversal sensing coil would be 

e^, = 1.59 X 10-9 X NIpi w cos wt + 1.59 x 10-9 nI^ V sin tot (4-4) 
The units of x and V are ft and ft/sec, respectively. 

The waveform associated with the first term is shown in Fig. 17(a) 
while that associated with the second is shown in 17(b). 

Clearly, the net induced voltage is not zero at the wire crossing. 
The extent to which this unwanted component degrades the position measurement 
will be discussed after a consideration of the voltage induced in the reference 

coi 1 . 

Consider the voltage induced in the reference coil when it is located 
midway between two laterally positioned wires (see Fig. 14). The function 
F(x, 0, 0.34) = 3.4 X lO-l^ weber/amp. both at and near this point (see Fig. 16), 
and 8F/9X = 0. The voltage induced in the N-turn reference coil is thus 

-66- 



* desired 

4 



l.3xlO''°Nim<^ 




(a) 



(b) 



location of wire 
® undesired 



^x 




3xlO''^NV 



sin Mt 



Fig. 17 Voltages Induced in the phase-reversal sensing coil. 



-67- 



®ref " 2*^ ^ 10"^^ NI^ 0) cos wt. 
As shown In Fig. 15, this quantity and e^ (as given by (4-4)) are multiplied 

to give m ^ o o 

em = 2.7 x 10-'^ N^ a)2 1^2 (] + ^os 2a)t)x 

+ 2.7 X lO-"'^ N^ 0) VIn,2 sin 2a)t. 

If the low-pass filter completely eliminated the terms at frequency 2w, then 

em = 2.7 x 10-19 n2(o2 1^2 x. 

However, to limit the delay caused by a first-order, low-pass filter to 
that which would cause an error of approximately 1/64" at 100 ft/sec, the 
filter time constant must be no more than 15 ysec or, equivalently, the filter 
corner frequency (fc) must be at least 10.6 kHz. 

Clearly, co must be sufficiently greater than wc so that appreciable 
attenuation of the 2a) rad/sec component is achieved. For example if f = 50 kHz, 
a filter with f^ = 10.6 kHz would attenuate the resulting 100 kHz component 
by 19.5 db. 

The net effect of the residual sin 2cot term in the input to the threshold 
circuit, is an indication of a wire crossing approximately 4 x 10"^ inches before 
the actual crossing (Here, it is assumed that V = 100 ft/sec). For all prac- 
tical purposes, this is negligible. If the wire-excitation frequency were 
greater than 50 kHz, this error v/ould be even less. 

The upper limit on this frequency is determined by practical considera- 
tions such as increased signal attenuation at higher frequencies. A choice 
of f =50 ^Hz has been a satisfactory choice in practice, 
b) Experimental Results 

The crossed-wire information source was evaluated using an instrumented 
test vehicle and current-carrying wires (f = 50 kHz) placed laterally across 
a roadway. The vehicle-borne equipment included a light-emitting diode and a 

-68- 



photo-transistor pair, mounted adjacent to a sensinq-coil configuration so that 
the emitted beam could be interrupted by an optically opaque rod projecting 
vertically upward from the test track. The frequency response of the optical 
system was sufficiently high that its delay contributed less than .02 in 
error for a vehicle speed of 100 ft/sec. 

Tests were conducted over a speed range from 29.4 to 88 ft/sec* The 
measured error (ex) is plotted versus V in Fig. 18, and it should be noted the 
errors are within a ±1/16 in band over the specified speed range. 

It is difficult to correlate these results with the predicted errors 
due to motion as the latter are so small (e.g., 4 x 10"^ ft for V = 100 ft/sec); 
however, as the measured errors are not much greater than the uncertainty 
associated with the measuring technique employed, it seems reasonable to attri- 
bute them to unavoidable experimental error. In any event, these errors are 
so small as to be negligible and an extremely accurate, discrete measure of 
vehicle position may be obtained. 

The wire-crossing information can be used to obtain an estimate of V(t) 
whereiri there would be two sources of estimation error: 

1) The uncertainty due to position quantization; and 

2) The number of missed counts (c). 

Since the wire spacing was 1 ft., the distance error in T sec would be 1 + c , 
and the velocity estimation error would be 

1 + c 

-y- (ft/sec). 

The probability of a missed count appears to be exceeding small, and this 
expression reduces to 1/T, 



*These and other tests were conducted by Michael Heslop and will be 
discussed in detail in both a forthcoming Master of Science thesis and a TCL 
working paper. 

-69- 



*i 

E 

o 



0) 

o 

o 
tn 

•o 

•o 
a> 

a 



o 



O 
O 



o 
o 

C 



> 
o 

z 






s- 



o 



o 

CD 



O 

m 



MX 



O 






c 
o 



I/) 
o 

o. 



00 



o 

5f 



CD 



K) '" 



iS 
^ 



O. 



o. 



o 

LlJ 



ro CM — 
o o o 



— cvj ro ^ »o CD 
9 O Q Q q 9 



-70- 



For T > 1 sec, this error would be small and thus an excellent measure 
of "average" velocity would be obtained. However, for T small, (e.g., T ^ 0.1 
sec), a large error could result. This approach would therefore not be satis- 
factory for the measurement of "instantaneous" speed, 
c) A Vehicle State Estimator 

Consider the achieving of position interpolation between intermediate 
position markers (see Fig. 12) and the estimation of V and A, This could be 
done by using unprocessed vehicle state information; however, as such informa- 
tion is often contaminated with undesired errors (e.g. bias errors, calibration 
errors, noise, etc.), it is generally desirable to employ some effective means 
of processing so as to achieve improved interpolation and/or state estimation. 

Two corranonly employed approaches, Kalman filtering^^ and adaptive fil- 
tering,^^ were not considered here as these generally result in complex processors, 
which presently appear to be unnecessary for a vehicle control application. 
Instead, a simpler approach, based on the concept of conditional feedback, ^^ 
wherein the signal errors are attenuated without affecting the desired quantities, 
is employed. 

Assume that the following measurement devices are available: 

1) A wire-detector and -counter to provide a 
measure of X + ex; 

2) A tachometer to provide V + ey; and 

3) An accelerometer to provide A + e;\. 

The terms ey, ey, and e/\, are errors in the measurement of position, velocity 
and acceleration, respectively. The six quantities specified have the following 
important properties: 

1) X, V, and A are obviously related; i.e. A = 



pV = p2x; 



-71- 



2) The measurement of X + ex is made at discrete 
intervals and thus is available in a sampled 
form (The sampling frequency is ^ where D is 
the nominal wire spacing and V is the average 
vehicle speed between adjacent wires); 

3) The mean of ex is zero for the sources of this 
error — detector noise, motion-induced voltage, 
inaccurate wire placement, etc.— would not result 
in an offset error.* » ** 

4) The signal e^ would be composed of both slowly 
varying and high-frequency components (These 
would result from tachometer miscalibration, 
variations in tire-rolling radius, wheel slip- 
page, and high-frequency noise which is 
invariably present). 

5) The signal e/\ would also be composed of both 
slov/ly varying and high-frequency components, 

as the accelerometer output would be significantly 
influenced by gravitational forces and vehicle 
motions and/or vibrations. 
These observations were utilized in the design, via the conditional feedback 
concept, of one possible state estimator (See Fig. 19). The estimator's inputs 

* The mean of ex is actually dependent on V; however, for the speed 
range of interest, it is less than 0.01 ft and thus is assumed negligible. 

** It is assumed that the probability of a miscount is negligible. 

-72- 



o 



(S) 
0) 



O 



II II 



o ^ o o 

10 o lo — 

11 '• "^ 'L 

'k) ^ «o O) 

:^ ic: :^ ^ 




O 

<o 

E 






•♦-> 
a; 



E 
Cr. 



U 

O 






o 

I 






are X + ey, ^' + ey, and A + e/\, and its outputs are continuous esti- 
mates of position (X), velocity (V) and acceleration (A). For the present, 
X + ex is assumed to be continuous; the effects of sampling are discussed 
later. 

These estimates are given by the following equations, which are readily 
derived from Fig. 19: 

2 . ^ P^ + (K2 + Ke) p3 -H (K2K4 + K2K6 + K5) pg ^ K2K3 p 

A ^ 

Kip3 + KiK6p2 + K1K3P KiK4p3 

+ ev + ex; 

A A 

V = V + PilJ^e ^ t^2P^ -^ (^1 -^ ^2^e) P^ -^ KiKfiP ^ 

A A 

(K2K4 + K5) p3 + (K1K4 + K2K3) p2 + K1K3P 

1 ''-' 

A A 

K6p3 + (K2K4 + K2K6 + K5) p2 + (K1K4 + K2K3 + KiKs) P + K1K3 
+ — ej^^ 

A 
where 

A = p^ +(K2 + K6)p3 +(K2K4 + K2K6 + K5 + Ki)p2 +(KiK4 + K2K3 + K-^Ks)P + '<iK3. 

Note that the desired quantities (X, V, and A) are unaffected by the estimator, 
while the measurement errors are attenuated by either low-pass, hinh-pass, or 
band-pass functions. 

The gains (K^, i = 1,..., 6) should be judiciously chosen to minimize 
effects of measurement errors, and to insure stable behavior. For the specific 
measurement devices used here, the gain values shown in Fig. 19 result in 

-74- 



low-noise and essentially unbiased* position and velocity estimates, and an 
unbiased acceleration estimate.** Note that high-frequency components of e/^ 
would be present in A; thus, low-pass filtering of A should be included as 
part of the vehicle controller. 



X+e 




Output =X^ex-X 



Fig. 20 Reconstruction of X + ex - X, 

As noted previously, X + Cv would be available in discrete form. A 

continuous position error X + ex - X may be obtained by using a samole-and- 

hold device as shown in Fig. 20. The modified estimator would be stable 

for — sufficiently large (i.e. the additional phase laq introduced by the zero- 

D 
order hold does not result in a phase margin <. 0°). For example, if the gains 

were chosen as in Fig. 19, the estimator would be unstable for I. < 5 Hz. For 

- . D 

small — s, some circuit modification would be necessary; one possibility is 

n 

discussed shortly. 



* In steady-state operation, the gxpected vaj[ues of X, ^, and A are 
X, V, and A respectively, and X - ^, V - V, and A - A are bounded; i.e., they 
are not accumulative. 



sense, 



** The K-|'s could have been chosen to be "optimum" is some statistical 

!. However, this would require a detailed statistical description of the 

errors, which is difficult (if not impractical) to obtain. At present, it 
suffices to employ K-|'s which are merely adequate. 

-75- 



The circuit, shown in Fig. 21, is one physical realization of the 
theoretical state estimator of Fiq. 19. The inputs are a pulse from the thres- 
hold circuit shown in Fig. 15, V + ev. and A + e^^. and the outputs are A. V 
and X. The latter is an interpolation of the distance between adjacent laterally 
positioned wires; i.e., X = X + the stair-step output of the wire-counter. 

For^> 10 Hz (e.g., D = 1 ft; V > 10 ft/sec) the circuit operation 

would be nearly identical to that of the theoretical estimator shown in Fig. 19, 

except that D is subtracted from the position output when a wire-crossing is 

detected. Then, X + e^ - X (= D - X) is sampled and held; after a negligible 

delay (= 50 ysec). Integrator A is also reset to X + e^ - X. 

For^< 10 Hz (e.g., D = 1 ft; V < 10 ft/sec), S^, S2, and S3 are 
D 
opened, and Integrator B is reset to zero to maintain overall stability. In 

this mode. V(t) would not be unbiased, and X(t) (X + the wire count) could 
contain small corrective steps at the instants of wire-crossings. If these 
steps were small (< .05 ft), and vehicles were not required to operate 
at < V < 10 ft/sec for prolonged time periods, this should not be a pro- 
blem. The potential accuracy (X - X < .05 ft and V - V < 1.0 ft/sec) and 
utility of these signals in constant-speed situations will be evaluated in 
full-scale experiments scheduled for 1977. 

It should be noted that a similar circuit, using only two inputs, 
X+e and V+e , has been employed in full-scale, vehicle-controller tests in 
which current-excited, crossed wires were the absolute position reference. 
In contrast to the circuit of Fig. 21 which provides X, V and A, this cir- 
cuit provided only X. 



* A portion of this circuit (Fig. 21) was employed in the "phantom- 
signal" controller tests which are described in Chapter VI. 

-76- 




«x 




II 

> 



a 
o 

CO 



o 
•♦-> 

E 
*j 
Q) 
Qi 



I/) 

(U 

x: 
•♦-> 

<4- 
O 

c 
o 

4J 
(C 
Ki 



Ol 



O) 



I/I 

o 

c 



CM 

cr. 



-77- 



D. Information Source 1— A Helical Transmission-Line Approach 

Each controlled vehicle can obtain continuous state information via 
helical transmission lines either embedded in, or located alongside, a roadway. 
This approach was introduced in an earlier report; ^^ here, following the more 
detailed account in Appendix B, the basic theory is presented together with 
the results from an intensive laboratory study. 

The spatially periodic, stationary, phase-difference (e^j) waveform 
shown in Fig. 22 can be obtained by properly exciting two helically wound 
transmission lines, detecting the field near those lines with two probes, and 
processing the detected signal (See Fig. 23). The wave period, Pg, is the 
"effective pitch length of the lines" and is a function of the individual pitch 
lengths P] and P2. A vehicle can use the information in this waveform to obtain 
a continuous position signal. Thus, a "coarse" position indication v/ould be 
obtained by counting the sudden 360° phase changes and a "fine" indication by 
measuring the linear phase difference between each pair of changes. In the 
context of the previous discussion, the former may be viewed as discrete sta- 
tionary markers.* 

a) Position Uncertainty 

The position uncertainty associated with this approach is proportional 

to the error in the phase-difference measurement. In the error-free case, 

ej 

^T = 360 ''e 
where Xj is the true position and fij is the true phase-difference. If the 
measured phase-difference (e^) were in error (i.e., e^i = Sj ± Bq) then. 



* A moving waveform can be achieved if one transmission line were 
excited at a slightly different frequency from the other. Then, the waveform 
would move longitudinally along the roadway at a speed v = Af Pg, where Af is 
the frequency difference. Each vehicle would be commanded to track a certain 
phase-difference valuQ and all vehicles would move in synchronism under normal 
operation. As this approach is less versatile than the stationary one in that 
changes in intervehicular spacing are more difficult to achieve, it will not 
be considered further. __ 

-/o- 



+ 180* 



-1801- 




Fig. 22 Theoretical phase-difference versus the longitudinal 
coordinate. 







*90*» 


- 


AMP 


— 1 pitch P| 






line 1 












b:>^\\\\\v--^- 


- \[ 








AMP 


1 , -U.. 




1 




1 ' 


t proue 1 






, 






1 
1 






GENERATOR 




1 
1 
1 


IV 


PHASE 


, ^r\ It, *\ 


lETER 


-^jj (Xpt) 










1 
1 






\ 




AMP 


1 » proDe d. 

— 1 1 

1 










llneZ 










AMP 


^^^^:^^:^::^ 


- i 






±9 0* 


-. 


1 

— ' 1 pitch Pg 












1 

1 , 








x^-0 





Fig, 23 Proposed longitudinal Information source using two 
hellcallv viouod tr»n«;mlss1on lines. 



-79- 



X = Xt ± Xp = — ^ Pp ± — ^ Pp 
^360 360 ^ 

Thus, the position uncertainty, Xg, would be directly related to the phase- 
difference error (6^) via 

X« = — P (4-5) 
^e 360 ^e- ^^ ^' 

Note that for a greater choice of Pg, Gg must be decreased for a given Xg. 
The phase-difference error is comprised of two components; Bgi which 
arises from obvious factors (noise, meter inaccuracy, etc) and ee2 which is 
due to lateral and vertical motions of the signal-detecting probes (See Fig. 
23). The latter is a function of the isolation between each probe and the 
"other" transmission line. The derivation of the equations governing this 
error is given in /Appendix B along with their experimental verification. An 
upper bound on 9g2 (i.e., 9g2 ) was obtained and will be used in the following 
analysis. 

Consider Fig. 24, where it is assumed that the lines are placed below 
the vehicle (the lines could be side-mounted but the maximum achievable separa- 
tion would be less). With 

±Az = the maximum lateral motion of the vehicle 
±Ay = the maximum vertical motion of the vehicle 
Vq = the nominal height of the probes 
d = the separation of the lines and of the probes,* 
then 9 results when the probes are at positions (1) in Fig. 24 as is 
demonstrated in Appendix B from which, 

^m 



* If the probe and line separations are not equal due to construction 
factors, this would be accounted for via a larger Az. 

-80- 



region of allowed 
'(OX probe location 

T" 

2 Ay 




Fig. 24 Line placement and the region of allowed probe location. 



where 

r^ = (Yq + Ay)^ + Uzf 
a^ = (d - Az)2 + (Yq + Ay)^ 
b^ = (d + Az)^ + (Yq + Ay)^. 

A plot of eg, vs.d for two extreme cases«-yQ =4", Ay = 3". 

^m r- oc 

and Az = 4". and y^ = 8", Ay = 6". and Az = 3"-is shown in Fig. 25. 

This can be used with Eqn. (4-5) to determine the necessary 
effective pitch and allowable tolerance on the vehicle lateral and 
vertical deviations. 

For example, to achieve a ±2" tolerance on Ay with Pg = 5 ft, 
then e < 12°. If such factors as noise, meter inaccuracy etc. result 



in no moi 



re than 5° of error, then 9. < 7°. Note from Fig. 25, that 



-81- 



Q> 



c 
o 



1. 
<o 

a; 
I/) 



a> 
a> 

^, 

a> 
•o 

E 

CM 
0) 

CD 




^O 



-00 



-CD 



-^ 



-CVJ 



— T 

o 

OJ 






— r 
o 



^:<i o 



"T" 



s. 

0) 

> 
o 

V 
U 

c 



I 

a; 

10 

a. 



c 

O 



in 

CSi 



C: 



o 



-82- 



d must be greater than 3 ft for the small -tolerance case and at least 
5.5 ft for the looser tolerances. 

b) Velocity Estimation 

An estimate of vehicle velocity may be obtained by counting the 
number of 360 phase transpositions in an interval of T sec and employing 

V = — ^ . (ft/sec) 
T 

Under constant-speed conditions, the estimation error would be 

T 
and, as 1 £ P £ 10 (ft), it would be unacceptably large for small T. 
A more desirable technique would be to employ the approach de- 
picted in Fig. 26. When a measurement were desired, a timer would be 
initiated and activated over T sec during which time n transpositions 
would be counted. In addition, the fraction of pitch length (f, ) 
traveled before the first transposition and the fraction (f„) traveled 
after the n transposition would be measured. The total distance 
traveled would be 

Under constant-speed conditions, an assumption of no missed 
counts, and with ±e , the phase errors in measuring f, and fp, the max- 
imum velocity uncertainty would be 

360 T 



-83- 



start of interval 



f|Pe 



[(n-D + VfgJPe 



H >- 

I I 
I I 
I I 



end of interval 



f^Pe 



Fig. 26 Interval for velocity estimation (elapsed time T). 
With parameter choices of P = 1 ft, T = .1 sec and 6^ = 12°, this max- 
imum uncertainty would be 0.67 ft/sec. If it were necessary to use a 
larger P , a corresponding reduction in 6 would be required to maintain 
the same uncertainty. 

c) On the Choice of Line Parameters 

It is impractical to completely "specific" the optimum helical 
line configuration (P-j , P , Pg, d) at this time, as this specification 
would depend upon other facets of the longitudinal control system. This 
would include the specification of tolerances on the permitted lateral 
and vertical motions of the vehicle, the allowable longitudinal posi- 
tion deviations, and the physical form of the roadway. With these 
data, the necessary design equations are available to then specify the 
optimum line geometry. 

At the completion of this study, it was discovered that a flat 
"helical line" appears to possess properties as good as, if not better 
than, the helical line. If so, a major cost factor (that of the manu- 
facturing and installing of the helical lines) will be circumvented. A 
variety of flat-line configurations will be evaluated under the contin- 
uation contract to ascertain a desirable shape for such lines. 

-84- 



E. Information Source 1 — Scattering Enhancement Plates 

a) Theory and Review 

A third approach for obtaining almost continuous position and velocity 
information is via a Doppler radar in conjunction vn'th enhancement plates 
embedded in, or mounted alongside, a roadv/av. This approach v/as previously 

16 2 8 

described, » and low-speed test results were oresented. 

In essence, enerqy is directed at a roadway surface by a vehicle-borne 
Doppler radar, and part of this enerqy is reflected back. When no plates are 
present, nonspecular reflection occurs, and the returned signal is contaminated 
with both amplitude modulation (AM) and frequency modulation (FM). This results 
in errors in the position estimate. When the plates are present (Fin. 27), 
specular reflection occurs such that the returned signal contains little or 
no unv/anted modulation, and an almost ideal Doppler signal 

e(t) = Eq cos [—-^ XjCt)] • 

X/(2 cos ap) 

results. Here, A is the wavelength of the radiation, Xj(t) is the instantaneous 

position of the vehicle relative to some reference point, and Op is the tilt 

angle of the enhancement plates. The amplitude, Eq, is essentially constant 

due to the regularity of both the reflectors and their spacing. In addition, 

the signal is enhanced if all returning rays are forced to constructively 

interfere. This is achieved by spacing the plates at intervals of nA/{2 cos Op), 

where n is an integer.* 

Since the phase of e(t) is proportional to X-p(t), the latter could be 

determined within an uncertainty of ±X/ (2 cos ap) by counting the number of 360° 

phase changes (This uncertainty could be halved if 180° phase changes were 

counted). For example, one change would occur ewery 0.65 in (1.64 cm) if 

a p = 30° and an X-band (10.5 GHz) radar were used. 

*Eo is a maximum for n = 1, however, this would require employing a maxi- 
mum number of plates. _85- 



Antenna beam 

T 




Roadway 
V^ V- surface 



Fig. 27 Behavior of vehicle-mounted Doppler radar 
with enhancement plates. 



b) Experimental Studies 

Both laboratory tests and field tests were performed during the period 
covered by this report. The latter were performed at the skid calibration 
pad at TRCO. Here, as is depicted in Appendix A, 370 aluminum plates (2 in x 
5/16 in) were positioned, with Op = 30°, in a 2-in wide wooden structure em- 
bedded directly below an asphalt-surface roadway. The plate spacing was 0.65 
in (1.64 cm), and the 20-ft structure was covered with an epoxy sealant. An 
X-band (10,5 GHz) radar, with an 18° (3 db) beamwidth horn, was mounted on a 
test vehicle such that h = 1 ft and Bl = 30° . Here h is the antenna height 
above the roadway and Bl is the "look angle" (See Fig. 27). 



-86- 



The results of low-speed tests (0 <. V £ 5 ft/sec) over this section of 
track were consistent with those from the laboratory; i.e., both a substantial 
increase (= 15 db) in backscattered energy and an almost ideal detected signal 
with no appreciable AM or FM resulted with the use of the plates. In addition, 
due to the slight curvature of the epoxy covering, water did not accumulate 
over the plates, and no loss of signal resulted when the tests were repeated 
under extremely wet conditions. 

Four months later, high-speed tests were conducted. However, during 
this delay, the covering had cracked, and some sections of the wooden structure 
had absorbed considerable moisture. A severe signal attenuation was encountered 
over those sections. Thus, in practice, weatherproof ing would be necessary 
for plates installed below the ground. If side-mounted plates v/ere employed, 
the problem should not be as severe as good drainage should be easily achieved. 

Additional tests were conducted with the plates located above the asphalt 
surface.* Here, a test vehicle was driven over the plates, and the detected 
signal was processed, via a counter, to indicate the number of 360 phase 
reversals. Two laterally positioned, current-carrying wires were used to define 
the beginning and end of a specified distance of some 6 feet, and a wire-crossing 
detector (similar to that discussed in Section C) was employed to activate the 
counter only over this distance. The vehicle was automatically steered, via 
the use of a wire- reference system, to insure that the radar antenna was always 
above the plates. 

In the first series of tests, ap = 20° , \/{2 cos ap) = 0.6 in (1.52 cm), 
and tests were conducted for speeds ranging from 7.3 to 88 ft/sec and 3l = 15, 
20, 30, and 40 deg. 



* In view of previous findings, the results obtained here should be 
the same as those obtained with buried plates. 

-87- 



One typical low-speed result is shown in Fig. 28 with e(t) in (a), the 
processed counter input in (b), and the processed wire-crossing, detected sig- 
nal in (c) (The latter specifies the counting interval). Mote that the returned 
signal over the plates was much stronger (= 15 db) than that over asphalt, and 
also that it v/as virtually free of both amplitude and frequency modulation. 
The presence of such modulation results in a loss of counts as can be seen 
from the processed "asphalt" returns of (b). The number of phase reversals 
counted over the specified distance was 121, and, as 121 plates were contained 
herein, a precise measure of distance traveled was obtained. 

The same results* were obtained from each test in this series: i.e., 
i) The returned signal over the plates was much 
stronger (= 15 db) than that over the asphalt, 
and it v/as virtually free of both AM and FM; and 
ii) The number of phase-reversal counts was constant 
at 121. 

In a second series of tests, the effectiveness of P|_ < 15° and 3l ^ ^-^ 
was evaluated. Consistent counts were not obtained, and it appears Bi should 
be maintained in the range between 15-40° to eliminate the need for a precise 
mounting of the radar and/or a JANUS configuration to account for vehicle 
pitch. ^^ 

The effect of removing plates (for possible reduction of construction 
costs) were examined in a third series of test runs. Here, one of each two 
plates was removed and then 3 of each 4. The procedure was identical to that 
previously described and tests were conducted for various combinations of V and 
6l within 7.3 < V < 88 ft/sec and 15° < Bl £ ^0°. 



* It was not possible to present similar data for a high-speed test 
because of the limited frequency response of the strip-chart recorder employed. 



-88- 






1 



1 



i^'~ 



Hfe 



V) 



g 

u 

c 
<o 

.c 
c 

0) 



n 
I. 

c 
o 
cr. 

s- 
o 

**- 

«o 

■4-» 

«o 



u 
I 



3 



■o 

Qi 
Q) 

a. 
to 
• 

o 



CO 
CM 



-89- 



Excellent results, a strona modulation-free siqnal and a consistent 
count of 121*. were obtained over the entire speed range and 

20° < 6l < 30° 
Thus, the allowed variation in 3l was reduced. If more than 3 out of 4 plates 
were removed (e.g., 7 out of 8), consistent results could not be obtained for 
any (V, Bl) combination. 

In a fourth series of tests ap = 45°, with all other conditions renaininq 
the same. The results were consistent with those reported here, 
c) Sources of Position Estimation Error 

In the ideal cause, one would have M counts for a distance X and 

X = Mq. 
In practice, the estimate would be 

X = X ± 6X 
where the position estimation error (6X) would be dependent upon three factors: 

1) The uncertainty in position due to quantization 
in units of q = X/(2 cos ap); 

2) The error due to the number (c) of missed (or 
added) counts; and 

3) The error due to random variations in X and/or 
ttp and thus in q. 

The contribution due to the first is q; and that due to the second, 
cq. The quantity c is difficult to estimate since no counts were missed or 
added in the experiments performed to date. As a strong signal is received 
from the plates, the signal-to-noise ratio is large, and the probability of 
a missed count should be yery small. 



* Note the system does not "count plates" but simply counts units of 
X/{2 cos ap) provided an approximately ideal signal of sufficient strength is 
received. __ 



The contribution from the third factor would be fJ6n, where 6q is the 
variation in q due to variations in X and/or ap. As variations in ap would be 
distributed about a fixed average value, the effects should cancel over any 
appreciable number of counts. Thus, <Sq should be influenced mainly by varia- 
tions in X. 

The composite 6x is thus 

6x = q + cq + H6q, 

and the normalized error over a distance X = Nq is 

6x ^ c + 1 ^ 6c[ 
Nq " ~ N q 

Consider a typical case wherein a 10.5 GHz radar with a frequency 
stability of ,^% (a common specification) is employed; ap = 30°, and the 
measurement interval is 1.3 ft. Here, q = 0.65 in, M = 24 and (Sq = .00065 

(due to changes in A only), and 

§1 _ .043 

Nq 

This error would be substantially decreased as X were increased; e.g., for 

X = 13 ft and N = 240, ^ = .0052 (If 180° phase reversals were counted, these 

ijq 

errors would be halved). 

If an incorrect count (c = 1) were to occur, the errors would increase 
to .084 and .093, respectively. In addition, if the Op variations did not, 
on the averaqe, cancel these errors would be .094 and .019, respectively, for 
maximum variations of ±1°. These errors would be an unrealistic worst-case» 
I.e. —these could be eliminated via a scale-factor chanqe. 



-91- 



d) Estimation of Instantaneous Velocity 

The precise position estimates available from this approach may be 
employed to obtain excellent estimates of a vehicle's instantaneous velocity 
provided an accurate time reference were available. One feasible approach is 
shown in Fiq. 29. Here, the processed Doppler signal would be the input to 
an auxiliary counter, which would be triggered "on" for an interval T by the 
time reference. The counter output (N) would thus be proportional to the 
average vehicle velocity over that interval. The later would be obtained via 

2 cos ap T 
In a constant-speed situation, the velocity estimation error would be 

2 cos ctp J 

assuming that no counts were missed per the previous discussion on position 
error. 

This error is independent of velocity and dependent on A, a and 

T. In practice, one should employ a yery high-frequency radar (i.e., 

X-baid or greater) so as to obtain a source/sensor configuration of a 

reasonable size. A practical choice would be a 10.5 GH^ radar (X = 1.13in) 

and, per the previous discussion, a reasonable plate setting would be 

a = 30 . Then the measurement accuracy would be 

X 1 1 

± _ = ±0.0544 - • 



2 cos ttp T * T 

This quantity is plotted versus T in Fig. 30. 

-92- 



Processed doppler 
signal 



rLTLTL 












Counter 


N 


Scale factor 


Vt 






^ 




I— J— _i 

Counting interval,! 







time 
jreferenc( 



Fig, 29 One realization of velocity measurement. 





Velocity error 










- 


(ft/ sec) 










0.50 - 


> 






A =l.l3in. 




- 








«-p = 30« 




0- 


■ i 


— r 


i 1 


1 1 1 


- — o- 

1 



0.5 



T(sec) 'O 



Fig. 30 Maximum measured error versus T— 
constant-speed case. 



-93- 



To obtain velocity with an accuracy of some ±0.5 ft/sec, one 

must select T £0.1 sec. Alternatively, one could count 180° phase 

changes for which the measurement accuracy would be 

X 1 1 
± 1= ±0.0272 _ 



2 cos ttp T T 
and select T <_ 0.05 sec. 

In a constant acceleration (deceleration) situation, the average 
speed over the interval would be measured and not the true speed at the 
end of the interval. This results in an error of ^ as is discussed in 
Section F. 

No experimental tests of this, or other suggested techniques, for 
estimating velocity were conducted during the past year. 

F. Information Source 1— A Fifth Wheel 



A fourth approach for obtaining position state information involved the 
use of a commercially manufactured fifth wheel.* This was not considered as 
a viable candidate for eventual implementation; instead, it v/as tested so 
that its accuracy as a position-measuring device could be established. This 
information would be useful, as it is sometimes necessary to use a fifth wheel 
in field evaluations of vehicle controllers because an installed information 
source is not always available. 

This wheel was connected to the rear bumper of a 1969 Plymouth sedan 
and evaluated under both constant-speed and constant-acceleration conditions. 
The former encompassed 11 trials at each of 4 soeeds (20, 40, 60 and 80 ft/sec) 



* This unit was manufactured by Laboratory Equipment Corp., Mooresville, 

Indiana. 

-94- 



for a tire pressure (Pj) of 22 psi (The lower limit specified by the manu- 
facturer, and 5 trials at each of these speeds for Pj = 35 psi (The upper 
limit specified). The latter involved tests with Pj = 22 psi and 35 psi. 
Those conducted with the lower pressure encompassed 12 trials for each of two 
speed-deceleration conditions~VQ = 20 ft/sec, A^. = 5 ft/sec^ and Vg = 60 
ft/sec, Aj, = -5 ft/sec^. The other tests included 5 trials for each of the 
same conditions. Data were collected only when the vehicle was operating 
either at a steady speed or at a constant acceleration/deceleration rate so 
that the replications, for a given condition, were conducted under nearly 
identical conditions. For example, the measurement interval for a decele- 
ration test was selected as shown in Fig. 31, 

m 




Measurement 
interval 



t=0 



t(sec) 



Fig. 31 Measurement interval during a constant deceleration test. 
This interval was selected as 100 ft, and it was delineated via the 
laterally positioned, current-carrying wires described in Section C. 
These wires v^ere laid on a fairly rough section of asphalt pavement. 

The distance traveled, as measured by the fifth wheel, was obtained 
as follows: 

-95- 



A circular gear with Nj teeth was attached to the 
fifth-wheel axis. As the vehicle moved, this wheel 
rotated and these teeth passed a pickup unit wherein 
the passage of each tooth was counted. This count 
was initiated at the beginning of the measurement 
interval and terminated at its end. The measured 
distance (D) was obtained via 

D = ri(^) (4-6) 

where R is the effective radius of the 5th wheel* 
and M is the total number of counts in an interval T. 

The results from the constant-speed tests are shown in Table XIJ( 
where the mean count (y) and standard deviation (a) are shown for each condi- 
tion. (These counts may easily be related to measured distance via Eqn.(4-6) 
with R = 1.0833 ft (for Pj = 22 psi) and Nj = 120). For Pj = 22 psi, the 
maximum ranqe of the means was only 0.06%, and the maximum standard deviation 
was a low 3.21 at 80 ft/sec. In terms of distance, the latter corresponds 
to a distance error of ±.18 ft in 100 ft. In the high-pressure case, the 
mean range was greater (0.27/^); however, (cj)niax ^^^s only 2.24 corresponding to 
a distance error of ±0.13 ft in 100 ft. In essence for a given tire pressure, 
extremely consistent and accurate results were obtained; however, the results 
varied slightly with pressure— being some 0.33% lower for the greater pressure. 



* This effective radius is a function of Pj and the tire-roadway 
interface. It can be specified by a simple calibration procedure involving 
(4-6) and a measurement of N from a field test over a known distance. 

-96- 



TABLE XIX 
FIFTH-WHEEL DATA FROM CONSTANT-SPEED TESTS 



Pt^ 

(psi) 


(ft/sec) 


20 


40 


60 


80 


22 


P 


1762.45 


1763.36 


1763.54 


1762.55 


a 


0.69 


1.12 


2.75 


3.21 


35 


y 


1755.20 


1757.40 


1756.20 


1760.00 


a 


0.84 


2.30 


0.87 


2.24 



TABLE XX 

FIFTH-WHEEL DATA 

FROM 

CONSTANT-ACCELERATION/DECELERATION TESTS 



Pt 


Vq. Ac 


Vq = 20 ft/sec 
Ac = 5 ft/sec2 


Vq = 60 ft/sec 
Ac = -5 ft/sec^ 


22 


y 


1762.36 


1766.00 


a 


0.92 


2.10 


35 


P 


1755.2 


1758.2 


a 


1.3 


1.30 



-97- 



The results from the constant acceleration/deceleration tests are shown 
in Table XX. For a given Pj, these are extremely consistent both within this 
test and across the constant-speed case. This is evident from a comparison 
of the data in the previous table with that presented here. Also, note that 
the results for Pj = 35 psi are aqain generally lower than those for Pj = 22 
ps i . 

The nonzero variance, for a given test condition, was probably caused 
by the bouncing of the fifth wheel and a corresponding incorrect count. 

Clearly, the fifth wheel may be used to obtain an accurate measure of 
X provided the distance involved is not great. As the error would tend to 
be cumulative, an error of 0.18 ft in 100 ft could correspond to an error as 
large as 1.8 ft in 1000 ft. In a vehicle controller application, where tracking 
errors (aX) of 0.5 ft are expected, such an error could cause a considerable 
offset in the estimation of AX. In such situations, a fifth-wheel estimate 
of X should be used very carefully and only over relatively short distances.* 

A measure of "instantaneous" velocity may be obtained using an approach 
similar to that described in Fig. 29. In a constant-speed situation, there 
would be two sources of estimation error: 

1) The uncertainty associated with position measure- 
ment; and 

2) The uncertainty due to position quantization. 

A conservative choice for the former is, from the collected data, 

TT^^T 



* The fifth-wheel estimate of X could be used in conjunction with 
other unbiased position estimates (e.g., that obtained from crossed wires) 
to eliminate cumulative errors. 

-98- 



where Dj is the distance traveled in T sec. Since the spacing between counts 

ttR 
Nt 



was -2^ , the total distance error in T sec would be 



1763 "T f!^ 
with a corresponding worst-case velocity estimation error 

1763 Nj T 

The maximum deviation would occur at the maximum expected speed which is 
assumed to be 100 ft/sec. Then, 

(AVl)max =1-25 ft/sec. 
(Here, it is assumed that Pj = 22 psi and the fifth wheel is calibrated, i.e., 
17.63 M = 1). 

Next consider the situation where a vehicle is decelerating (accelerating) 
at a constant rate over at least T sec as is depicted in Fig. 32. Under ideal 
conditions, the measured velocity at t + T would be 

V = V(t)jJ^it_M2 
2 

which is — units too large (for V(t) > V(t + t)). Thus, under nonideal con- 
2 

ditions, the worst-case velocity estimation error would be 

AVl = ± Ji- V ± M 1 ± AI (ft/sec) 
1763 Nt T 2 

The maximum error would occur when the vehicle were decelerating at a maximum 
permitted rate. For A =12.88 ft/sec^ and the parameters previously employed, 

(AVl)max = l-S^ ft/sec2. 
If this were too high, a lower value eould be achieved by increasing Nt and 
insuring that the percentage of missed counts remained the same. 

-99- 




v(t*-n 



t ^T/2 



t+T 



Fiq. 3? Measurement interval for a vehicle 
decelerating at a constant rate. 



In essence, the commercially available fifth wheel which was tested 
here, can be used to obtain an accurate estimate, within ±1.89 ft/sec of the true 
value, of "instantaneous" velocity in all expected operational situations at 
the critical high speeds 80-100 ft/sec which are of great interest. This 
estimate would be within ±1.42 ft/sec provided A were limited to ±3.22 ft/sec^. 

Clearly this fifth wheel, which is a typical correnercial model, can be 
used with confidence as a source of state information for vehicle controller 
tests— provided its limitations are properly considered. 

Beyond the merits of the specific wheel studies, it has been suggested 
that an "internally mounted" fifth wheel be employed to provide state infor- 
mation in an operational situation. Based on the results presented here, 
this could, with a proper design, result in excellent position estimates 
(especially if an unbiased updating measure were also provided) and velocity 
estimates with an accuracy of some ±1 ft/sec. 



-100- 



G. Information Source 2 

In theory. Information Source 2, which would be intended to provide 

information directly from the roadway to the sector computer, would not be 

needed as all necessary functions could be handled by the roadv/ay-to-vehicle/ 

sector-computer combination. However, it would be highly desirable to have 

such an information source for purposes of redundancy. 

Durinq both the first and second years of this study, various approaches 

toward the realization of an adequate configuration were considered—some of 

which were listed previously. ^^ In essence, none of the suggested approaches 

would result in vehicle state information to the same precision as that 

obtainable from the Information Source 1 configurations discussed here. This 

is an area in which much future effort should be expended. 

H. Conclusions 

Four approaches for providing individual vehicles with longitudinal 

state information have been evaluated and their performance limitations 

specified. 

a) Crossed-Wire Configuration 

This configuration could be effectively used 

to define intermediate position markers with 

marker intervals in the range of 1 to 100 or more 

feet. The measured position at a wire crossing, 

per the results presented here, would be within 

0.0052 ft of the true position for speeds from 

0-80 ft/sec (and probably for higher speeds as 

well). However, the velocity estimates derived 

from the crossings would not be a sufficiently 

accurate measure of a vehicle's "instantaneous" 

velocity. 

-101- 



The latter could be obtained by using a 
conditional feedback approach wherein the signals 
from the crossed wires, a tachometer and an 
accelerometer would be employed.* 
b) Helical-Line Configuration 

Properly excited helical transmission lines 
could be employed to both define the IPM's and 
provide a distance interpolation bet\"/een these 
markers. The position measurement accuracy, oer 
laboratory tests only, is some .17 ft for the 
particular parameters considered in Section D— 
a result which should be speed independent. 

Various approaches for obtaininn a velocity 

estimate from these lines were considered. If P 

e 

were small and a reasonable accuracy were present in 
the phase measurement, "instantaneous" velocity could 
be estimated to an accuracy of some 0.9 ft/sec provided 
|A| < 3.22 ft/sec. 

A potential problem with the use of these 
lines involves the difficulties associated with 
their manufacture and roadway installation. These 
may be overcome by using planar lines v/hich, after 
preliminary tests, appear to possess the same 
signal characteristics as the circular lines. 



* This approach was employed in a series of field tests of a crossed- 
wire configuration (with 1 ft between each wire pair)/vehicle controller 
combination. 



-102- 



c) Scattering Enhancement Plates 

These plates can be used to provide both an 
accurate position signal (e.g., a maximum posi- 
tion error of ±.05 ft in a 10-ft distance) and 
an estimate of instantaneous velocity which is 
within ±0.7 ft/sec, provided |A| < 3.22 ft/sec^, 
over the speed range 0-100 ft/sec. 
Thus, they could be used for both position inter- 
polation between IPf^'s, and to provide an accurate 
velocity estimate to compare with a threshold 
value for emergency detection purposes. 

d) A Fifth Wheel 

When a permanently installed information 
source is not available, the fifth wheel 
evaluated (a standard commercial model) can be 
used as an accurate source of state information. 
Distance estimates obtained over a 100-ft interval 
were accurate to within ±.34 ft, and instantaneous 
velocity estimates should be accurate to within 
±1.4 ft/sec for speeds from 0-100 ft/sec, provided 
|A| < 3.22 ft/sec.^ For |A| < 12.88 ft/sec^, the 
latter should be accurate to within ±1.9 ft/sec. 

Based on these results, an "internally 
mounted" fifth wheel could be employed to provide 
state information in an operational system. With 
a proper design, oosition estimation errors within 

-103- 



±.1 ft for a 100-ft interval, and velocity esti- 
mates within ±1 ft/sec of the true value should 
be achievable. 

None of the approaches specified for an Information Source 2 would 
result in vehicle state information to the same precision as that available 
from the configurations listed above. This is an area in which much future 
effort should be expended. 



-104- 



I 



Chapter V 
ON THE IDENTIFICATION OF VEHICLE DYNAMICS 

A. Introduction 

In the design of a vehicle longitudinal controller, both braking and 
propulsion aspects must be considered. For realism, one must employ a valid 
model of both the braking and the propulsion roadvay- interface dynamics. 
Othervn'se, the desired performance characteristics, which would be incorporated 
into the design, would probably not be achieved by the corresponding physical 
implementation. Here these dynamics, which were obtained from full-scale 
tests, are specified for a U.S. passenger sedan. 

B. A Model of Braking/Roadway- Interface Dynamics 

The relationship between a brake actuating signal (V-j) and a vehicle's 
speed is dependent on such factors as the condition of the brakes, the pro- 
perties of the tire/road interface, and the vehicle's deceleration rate. 
This relationship is nonlinear and quite complex. As the goal of the effort 
reported here is the design of a closed-loop braking system, it is probably 
not necessary to employ such a complex model, and a much simpler one, involving 
an input-output relationship for an expected range of vehicle speeds and 
deceleration rates, could be adequate. 

One simple model is shown in Fig. 33. Its parameters Kb, a, 3, 6 and 
T are assumed to be a function of condition (i.e., a fixed command deceleration 
rate (A^) from an initial speed (Vq)), thus partially accounting for the non- 
linearities in the braking dynamics. This model was selected after an examina- 
tion of data obtained from braking tests. 

-105- 



Vi 


Kge-P'^ip+S) 


V 







Fig. 33 A simple model of bra king/ roadway- 
interface dynamics. 



The model parameters were specified for a 1969 Plymouth sedan by 
matching braking responses (aV vs.t), obtained under full-scale conditions 
from the configuration of Fig. 34, to the responses of a corresponding ana- 
log simulation model.* Three typical results are shown in Fig. 35 where both 
model and full-scale responses for the input command 

Vc(t) = Vo t < 

Vc(t) = Vq - 14. 5t < t <. Vo/14.5 
are shown for three initial speeds— 20, 60, and 90 ft/sec. The following 
observations were made from both these and other responses obtained from 
different braking situations: 

1) The response changes with Vo(e.g., the time at 
which the peak value (AVm) occurs increases with 
increasing Vq); 

2) The magnitude of the response does not increase 
linearly with increasing Ac; and 

3) The form of the response changes with Vq and/or Ac. 



* This presentation is a summary of the more complete treatment con- 
tained in Appendix C. 

-106- 



Thus, the braking dynamics are a nonlinear function of, at least, Vq and Ac; 
however, t appears to be nearly constant at some 150 m sec. 



^c, -r^ ^\ 


1.0 


^i, 


Vehicle 
or 

Model 




V 


\ 


y 






*" 


1 











Fig. 34 Closed- loop system employed in the 
parameter-identification process. 



The composite results are shown in Table XXI where V/V^- is defined for 
20 (Vq - Aj.) combinations. The nonlinearity of the braking dynamics is at 
least partly shown here. Thus if the model (and the braking dynamics) were 
linear, the quantity -A_ would be invariant with respect to both Vq and A^. 
Instead, as is shown in Fig. 36 where Kg6/a3 is plotted versus Vq with A^ as 
a parameter, this quantity varies over a range from 2.63 to 1.25. 

A considerable amount of variability was presented in the recorded 
responses. Thus, while AV^ = 8.5 ft/sec in Fig. 35(c), it ranged from 7.6 to 
10.5 in other tests conducted under identical conditions. This variability 
is easily accounted by specifying a range of Kq for a given (Vq - A^) combina- 
tion. The observed changes in Kg were some ±20% of the values specified in 
Table XX; thus, in designing a closed-loop braking system, one should design 
for an insensitivity to changes of at least this magnitude. 

The model predictions correlated reasonably well with data obtained 
under both wet- and dry-road conditions; however, in some situations, generally 
those involving large deceleration commands and a very wet road surface, poor 

-107- 




— Full-scale result 
X Model predictions 



— 1 1 1 1— 

Time (sec) 10 



a) Vq =» 20 ft/sec. 



X ^ 




1 r 

Time (sec) 







1^ 
5 



b) Vq = 60 ft/sec. 



T T r 

Time (sec) 








10 



c) Vq = 90 ft/sec. 



Fin. 35 Comparison of vehicle response and model response 
for 3 selected Initial speeds and Ac = 14.5 ft/sec^ 
(Dry- pavement conditions). 



-108- 



o 



O 
CX3 



O 



O 



o 
evj 




ID 



ID 



O. 

in 



+ 



LT) 

Q. 
LO 

• 



+ 

c 



LO 







LO 

+ 

If) 



+ 

Q. 



If) 



O- 



un 



ID 
CM 



ro 



+ 



Lf) 



lf> 

^1- 



ro 



ro 

+ 



+ 
Cl 



LD 



Ko 



ID 



+ LD 

O. • 



+ 

ex. 



LD 



in 
ro 

+ CL 

o. 

I^ LD 
ID 

• CM 



ID 

ro 

+ 



+ 



ID 



+ 



• CM 






vo 



ro 


<»-^ 




+ 


ID 


. — ^ 


C- 


fo. 


"5- 


»— ^ 


• 


+ 


•-*». 


p— 


C- 


ID 


+ 




• 


Q.^ 


CM 




no 


+ 


CO 


+ 


CL 


• 


O- 


•— ^ 


«;3- 


>— ' 



D. I— 



ID 



+ 

CL 



o 



ID 

+ 



+ 

CL 



CM 

00 



ro 



CL f— 



ro 

+ 



LD <:r 



+ 
oJro 



LD 
ID 



c 

CH- 



ID 

1^ 



+ 

Q. 



ID 
LD 



«3- 
+ 
CL 

ro 

+ 

CL 





LD 



ID 



CC 



C t— 



|ro 

+ 

CL 




c 
o 



o 

u 



(O 



o 



u 



o 

LO 



II 



2Z 



+ 

CL 



CO. 

+ 
c 



C- 



X 
X 



C3 



4< 

51- 



cc 



in 

or 

LlI 






o 
c 



i 
i 









00 
00 

• 

CM 



c 

ID 



-109- 






3.0- 
2.0- 
1.0- 



0- 



Xoo-h 



— I — 

20 



■•■a 
Xo 



o 
o 
X 



40 60 

Vjf/s) 



Ac(f/s2) 
6.44 

9.66 
12.88 
14.5 



^ 



100 



Kr6 
Fiq. 36 -At vs. Vn with Ar as a parameter. 



correlation was obtained. This is shown in Fig. 37 where AV vs. t is shown 
for Vq = 40 ft/sec and Ac = 12.88 ft/sec. Note that wheel lock occurred, 
and the braking system responded in an antiskid mode. The resulting response 
was highly oscillatory, and quite different from the predicted response. If a 
more efficient antiskid mode (one that would have resulted in minimal ampli- 
tude oscillations and a more comfortable stop) had been employed, the model 
response would have been a fair approximation of the full-scale response. 
Thus, if the large oscillations of Fig. 37 were greatly reduced, the response 
shown in Fig. 38 would result. This response compares favorably with the 
model response which is also shovm. 

C. On Braking Controller Design 

The model specified here results in predicted responses which are rea- 
sonable approximations to corresponding full-scale responses over the speed 
and acceleration ranges of interest. Thus, it should be useful in the design 

-110- 



AV 
(ft/sec) 




Time (sec) 



Fig. 37 Vehicle response for Vq = 40 ft/sec, 
A^ = 12.88 ft/sec2 and wet-pavement 
conditions. 




Assumed full-scale response 
X Model response 



Time (sec) 



Fig. 38 Assumed full-scale response with an 



efficient anti-skid mode. (V, 



40 



ft/sec, Ac = 12.88 ft/sec2 and wet- 
pavement conditions). 



-111- 



of a braking controller; however. In viev/ of the variability of the recorded 
responses, which can be modelled by changing Kg from the value specified for 
each Vq - A(- combination, the controller should be designed for insensitivity 

to a highly variable braking gain. 

An efficient anti-skid mode should be incorporated into the design so 
that adequate braking performance at rates up to 12.88 - 14.5 ft/sec^ could 
be achieved on both dry and wet pavement. The specified model could be 
employed in this part of the design, as it should provide a reasonable aoprox- 
imation to the response in a well-controlled, anti-skid mode. 

It should be emphasized that the specified model was selected because 
of its simplicity and potential for use in the braking-controller design pro- 
cess. Another model, with more accurate predictive properties, may be specified; 
however, it would probably be characterized by a fairly complex, nonlinear 
differential equation and be more difficult to use in this process. 
D. Vehicle Propulsion Dynamics 

In a previous study, ^^ the propulsion/roadway interface dynamics of 
a 1969 Plymouth sedan were specified and subsequently used in the design of 
a vehicle longitudinal controller. During the past year, it was desired to 
test this controller in conjunction with the "crossed-wire" information source 
discussed in Chapter IV. This controller was implemented on a 1965 Plymouth,* 
as it was equipped for automatic steering which was necessary to keep the 
vehicle over the crossed wires. 

During a full-scale evaluation of this controller/ information source 
combination, it was observed that the vehicle response was inferior to that 
obtained from a simulation model of the vehicle model /controller combination. 



* The 1969 Plymouth is not presently instrumented for automatic 
steering. -112- 



This was due to the inadequacy of the model which was not valid for the 1965 
Plymouth. It thus became necessary to develop a model for this vehicle so 
that a more effective controller could be designed. 

Consider the model shown in Fig. 39. This relatively complex, velocity- 
dependent model* is one possible simplification of a more complex model in 
which such phenomena as a transport delay in the fuel-air system, lags asso- 
ciated with the propulsion system-drivetrain combination, the nonlinear effects 
of slipping tires, and the variety of forces which act, linearly and nonlinearly, 
on a moving vehicle, are explicity included. 



Vi 


Kp(v)(j(v)P^ 1) 


Vw 

► 


1 


^^ 




(7{;;)P*l)(.l67p.)(p..05) 


fwP^' 





Fig. 39 A velocity-dependent model of vehicle propulsion 
system/roadv/ay interface dynamics. 



The model input is V^ v/hich, in practice, would be the input to an 
actuator controlling the throttle- valve position. The quantity Vy; is the 
driven-wheel velocity as measured via an onboard tachometer^* and V is vehicle 
velocity with respect to an inertial frame of reference. (This was obtained 
via a fifth wheel; i.e., it was assumed that V5 = V). Three velocity-dependent 
functions Kp(V), y(V) and C(V) are included. The first tv/o are associated 

with nonlinear effects in the propulsion-drivetrain combination and the third 

* This model is more complex than that previously specified for a 
1<569 Plymouth. ^^ The additional complexity was necessary to provide a qood 
match betv/een model response and full-scale responses. 

** This is not to be confused v-ith Vj which was previously defined as 
the velocity measurement obtained from a nondriven (braked) wheel. 

-113- 



with the tire-roadv/ay interface. Average values of the latter,* which were 

specified in a previous study, are shown in Fig. 40, 

The quantities Kp(V) and ^(V) were determined via a model -matching 

approach, in which the following procedure was employed: 

The command input, V^ = 2t (ft/sec), was applied to the 
controller/ vehicle system shown in Fig. 41, while the vehicle 
was initially traveling at a fixed speed, and the signal e(t), 
which is defined in this figure, was recorded. This proce- 
dure was repeated several times at that speed to verify that 
a true response indication was obtained. This was done for 
eleven initial speeds: 0, 5, 10, 20, 30, 40, 50, 60, 70, 80, 
and 90 ft/sec. 

The full-scale tests were subsequently replicated using 
an analog computer. The system model was excited with the 
same command, and the response e(t) was matched with that 
obtained in the corresponding full-scale test by appropriately 
adjusting Y and Kp. Thus, these quantities were assigned 
values for each selected speed. 
Typical full-scale and model responses are compared in Fig. 42. Three 

comparisons are shown, corresponding to initial speeds of 20, 40, and 80 ft/ 

sec. Note that good correlation exists in each case. 

The composite results Kp(V) vs. V and Y(V) vs. V are specified in Figs. 

43 and 44, respectively. Note that both quantities change substantially with 

V ( as does ^(V), which was shov/n in Fig. 40). These results are generally 



* In the model for the 1969 Plymouth, a lov/er bound on ^(V) was employed 
to allow for a worst-case phase lag. Since C(V) is now included as a zero 

(phase lead) in _)1 , a lov/er bound would not result in a worst-case condition. 

-114- 



5(v) 



10" 



5" 



0- 







H 1 • 1 • 1 -H 1- 



20 



40 



60 80 

V (ft/sec) 



100 



Fig. 40 ^(V) versus V (obtained from Reference 16) 



-115- 





— ^ 


2.38 
P 




>^ ''' . 












M= ,/:>e(t) 






(^ 


Vehicle 
or 

Model 


Vw 


^ 

1 




r 










46.7 

































Fig. 41 Velocity controller used for modeling. 



consistent with those previously specified for a 1969 Plymouth, and emphasize 
the need for accounting for nonllnearltles when dealing with rubber-tired 
vehicles driven by Internal combustion engines. 

This model was used In the design of the position controller, which Is 
described in Chapter VI. Although this controller resulted In small tracking 
errors, the full-scale responses deviated somewhat from the corresponding 
model responses as is subsequently discussed in detail. 

These deviations may be overcome by employing a more complex model. 
Such a model, which is currently being evaluated (Nov. 1976), is shown in 
Fig. 4 5. Note that Kp = Kp(V, V-j ) and y = Y(V, Wg, wt) where we is the engine 
speed, and w^ is the torque-converter turbine speed. With such a model, one 
should be better able to predict various phenomena (e.g., the existance of 
a lov/-speed limit cycle) which result from the nonline&rities Inherent in the 
vehicle dynamics. 

-116- 



Model responses 



Vehicle responses 



f 












''''Vt 








































1 ft/sec 






■ i^' 












A 


■ I** 




■}]^ 








p~ 








t 




n i i 1 






...» 


















.:;: 






























: :.; I 




; . , : 






■ :i+ 


tiit: 


jtjf 




3# 



IsecH r 




(a) V=20 ft/ sec 





r: : : 




:U±1- 


r.: i: 


::it:i:' 






















*"4i 












^-Ut 








^^ii: 




-tik 






p 






^ 




■;■: 


f;:; 






rrfJ- 








V:-A 










~Bt 










^"^-T-i- 




■- * : ; 








■ Irrt 










inl 






.:;i;. 






l-fr 


;: : ; 






r.:rj 




[■-.'' 




: Hr 




i: :.v 




r::l 










(b) V= 40 ft/sec 







(c)V=80 ft/sec 



Fiq. 42 Comparison of model and vehicle responses, 



-117- 



Kp(V) 



0.20- 



0.10- 








80 100 

V (ft/sec) 



Fig. 43 Kp(V) versus V, 




80 100 

V (ft/sec) 



F1g. 44 Y(V) versus V. 
-118- 



Fig. 45 A more complex model. 



-119- 



CHAPTER VI 
A VEHICLE LONGHUDIMAL CONTROLLER- 
DESIGN AND EVALUATION 



A. Introduction 

A longitudinal control system for an individual vehicle must be designed 
so that the following general requirements are satisfied: 

i) Physical realizability — any required response 

must be within the capabilities of the vehicle; 
ii) Passenger ride comfort (|Jerk| < 1.6 ft/secr in 
online operations); 
iii) A small vehicle- position error (< 1 ft) under all 

input conditions; 
iv) Minimal effects from disturbance inputs; 
v) A minimal ramp length for entry merging maneuvers; 

and 
vi) A quick and accurate response to an emergency 
command input. 
These were previously discussed in detail, ^^ and a preferred controller type 
specified. This was a position controller, as good control of a vehicle's 
position would result in correspondingly good control of both its acceleration 
and velocity. 

Consider the position controller shown in Fig. 46. It is characterized 
by command inputs Xc(t), Vc(t) and Ac(t), a disturbance input and a single 
output X(t). In view of the discussion in Chapter IV, longitudinal state 

-120- 



information should be available to each vehicle in either a continuous or 
near-continuous form. Therefore, the controller should be designed to res- 
pond to such inputs. 

Previously, a controller with excellent performance characteristics 
was designed for a 1969 Plymouth sedan and evaluated under field conditions. ^^ 
Here, a fifth wheel was employed to measure the required state variables. 
In the studies of the past year, it was desired to evaluate this controller 
in conjunction with the crossed-wire information source and a state estimator 
similar to that discussed in Chapter IV. A 1965 Plymouth was employed as it 
was instrumented for automatic steering (This was necessary to maintain the 
vehicle over the crossed wires). The previously designed controller, when 
installed in this vehicle, did not result in satisfactory performance, and it 
was necessary to design the controller discussed here. 




M-t 



1 I 



Compensating 
Elements 

n r 

V A 



Vi 



Disturbance 



Vehicle 



V 



Fig. 46 General position controller. 
B. Controller Design 

The controller shown in Fig. 47 was selected for reasons of simplicity, 
the availability of all required feedback variables and inputs, and its general 

ease of implementation. 

-121- 



12 

1- 

Q. 



CVi 



ID 
CO 

cvi 

+ 

a. 



in 

+ 

Q. 



II 



o 






£ 




cj 




■M 




to 




>> 




«/) 


(0 


^_ 


• 


o 


^ 


L. 
4-> 




C 

o 
u 


•> 




^ 


«o 




c 


<D 


•f— 




=3 
4-> 




•r- 


m 


cr. 


(P 


c 
o 


csl 


'~ 




Q) 


> 






x: 


N" 


0; 

> 


csj 

• 


<x 


II 






r«. 


:^ 


^ 


t 


• 

•r- 


h- 


U. 


^ 




(0 




II 




i^ 





-122- 



The inputs are X^, V^ and A^, and X, V, and A are employed for control 

purposes. The latter three would be available as estimates: X, V and A, 

respectively. If an appropriate state estimator were used (See Chapter IV, 

Section C), X and V would be unbiased and relatively noisefree, and 

X = X and V = V. 

As A would contain a substantial amount of high-frequency noise (e.g., that 

due to vehicle vibration), the function ( — \ \r ) was selected to appropriately 

p + lb 

filter Aq - A. Then, one may assume 

A = A 
with no appreciable effect on the controller design. 

The composite linear compensator Gc(p) was selected to insure small 
position errors to both ramp- and parabolic-position commands. The nonlinear 
compensator, which is detailed in Fig. 48, was selected to nullify the velocity- 
dependencies of Y and Kp which were specified in the previous chapter. The 
piecewise-linear approximations for -i- and — shov/n in Figs. 49 and 50 v/ere 

i^p y 

employed, and the resulting linearized propulsion model v/as 



Glin(p)= 



- V 1 1.19 



Vi* (0.07p + l)(0.167p + l)(p + 0.05) ^ 

Internal velocity feedback was used to speedup the response of this 
linearized model, and to reduce the effects of model inaccuracies at low 
frequencies ( 0.1 rad/sec). The resulting transfer function was 

X ^ /i V ^^Mn (P) \. 102 

Vi** "Vp/V + f^lin (P)/' P(P + 15)(d + 2.65)2 ' 

where V^-** is defined in Fig. 47. 

The selection of 

G fn) - ^-(P + 2.65)2 (p + 1.5) 
^ d(p + 15)2 

-123- 




O 
♦J 
<ts 

lA 

C 

o; 

a. 
E 
o 
u 

s. 
<a 

04 



o 

c 



CO 



-124- 




x= experimentoi values 



V (ft/sec) 



100 



Fin. 49 A linear approximation of — • 



(sec) 


t 




















.40 


**^-^ X 


^■"^ 


x"^ 
















.20 


< 






X 


v^ 


x^^ 


X^^v.. 


'•v>^ 


X 




o-\ 








' 












— •— ^ 



20 40 



60 



80 100 

V(ft/sec) 



1 



Fig. 50 A piecev/ise linear approximation of — . 



-125- 



resulted in the root loci shown in Fiq. 51, where the open-loop transfer 

function was 

r rn> - in2K (p + 1.5) 
p2 (p + 15)2 

Note that K = 6.67 would result in adequate damping and a fast-resDondinq 

system. As this is a Type 2 system, the steady-state position error to a 

ramp-position (constant- speed) command is theoretically zero. 

The response (Xe - X) of a simulation model to the move-up, maneuvering 

command 

Xc(t) = X(0) + V(0)t + t2, (0 < t < 5) 

which was applied to a vehicle initially moving at a constant speed, is shown 

in Fiq. 52(a). The response peak is 0.45 ft, and Xc - X quickly approached 

zero after the maneuver was completed. Note that this response should be 

speed independent. 

The response to a disturbance input, equivalent to a sudden 44 ft/sec 
headwind, is shown in Fig. 52(b). The response deviation reached a maximum 
of .25 ft and thereafter rapidly decreased to zero. Thus, this design is 
relatively insensitive to such inputs. 
C. Full-Scale Tests and Results 

The simulation studies were followed by partial full-scale tests, which 
were conducted on a high-speed test track using an instrumented 1965 Plymouth 
sedan. The longitudinal control functions — braking and acceleration — were 
accomplished using electrohydraulic actuators. An analog computer consisting 
of 22 operational amplifiers, 15 potentiometers, and other necessary components 
was installed over the back seat. The computing elements were used for command 
generation, state estimation and data collection. Controller compensation was 



-126- 






h- 


CM 


iO 


-" 


(0 


II 


II 


^ 


^ 



ro ^ 
to 

II 



LT) 



CM 



CM 

Cl 



o 






cr. 

c 

"5 

c 
o 
o. 
(/) 
0) 

u 
i~ 
o 

o 



en 

3 
U 

o 



s 






4 O 

CM 



o 
o 
a: 



to 

en 



-127- 



T 
Ift 

jL 



-^ 






— 


5 sec 




f-- 










Ixi; 














i--J 


:-:f 




■?;-;.; 




lU' 




J>rr 


n^ 




::;: : 


Wf 




fM^ ^W 




i:':': 


-ml 

■t-n - 




HH 


iTii" 






-t~i^"'" 










T '- • 


i?tl 






; , .- 




HH 


«:!■ 


lit;" 


IrHr 










-M 






: : : p 





( Q ) Response to o maneuvering command 



Ift 





.t4--Vt 






>s 


ec 






■: - ' ! 








:zil 


■:; ;; 






HTr 






llH 


i;-^^ 












k-- 


... i :. 








\.: 


.; ;.t 








iir' 










'\\-i 


;-vT: 










;.: .■ : 


•:;;t 


i:: -. 








":;■:" 


~:-rr 


' *-t ■ 


H^ 




r;Ti 


i; .' f 


li:\ 


-rtrt 
•lit. 


"I : . : 







(b) Response to a 44 ft/sec step headwind 



Fig. 52 Simulation responses (Xc - X) to a maneuvering 
command and a disturbance input. 



-128- 



accomplished via a circuit, which was separate from the computer. All collected 
data were recorded on a 6-channel, strip-chart recorder located next to the 
driving position. The acceleration and velocity were measured by an accelero- 
meter and a fifth-wheel tachometer, respectively. 

All of the roadway-based equipment required for a complete full-scale 
test was not available, and thus the command quantities (X(., Vq and A^) 
were generated onboard the controlled vehicle and the estimates, (X, V and A) 
were obtained by appropriate processing of V5 and A/jqc;, the accelerometer 
output. 

One practical processor is shown in Fig. 53, The estimator portion of 
this processor is essentially equivalent to the state estimator of Fig. 21 
with $1, $2, and S3 opened, and the command portion is an analog equivalent 
of the digital command generator discussed in Appendix D,* 

If one sets 

V5 = V + ey 
and 

Aacc = ^ + e;^. 
then the state estimates (X, V, and A) are easily derived from Fig, 53 as 



2p p2 + 2p 

2p + 2 p 

P' 

2p + 2 1 



A = A + -5 r r ey + -5 r r en ; 

)2 + 2p + 2 ^ p2 + 2p + 2 "^ 



V = V + -s r ew + -5 ea ; 

)2 + 2p + 2 ^ p2 + 2p + 2 ^ 



' = ' " p(p2 + 2p + 2) 'V ^ p2 . 2p + 2 ^^- 

Mote that X, V, and A are unaffected by the circuit. Per the discussion in 
Chapter IV, Section C, ey and e;^ would contain both bias (or slowly-varying) 



* One objective of this study was to determine a suitable value for 

the command sampling interval Ts; thus, an analog command generator v/as used 
since it would have been difficult to vary Ts in a digital one. However, in 
an operational system, a digital command generator would be employed to satisfy 
accuracy requirements. 

-129- 




0> 





0> 




i- 




E 




o 

4J 


. 


o 






k. 






^ 


(1) 


o 




•^- 


•^' 






4J 


0) 


a 




(/) 


£ 


•^ 




01 


o 


1^ 




(U 


w 


a> 




4J 


a> 


4) 






a> 


^ 




Ui 


o 


^ 




-o 


o 


1 

x: 




c 




^- 




t. 


o 


«*- 




o 


«^ 










> 


s. 


b 


o 


— 


c 


2 




O 




«*- 


E 


II 


X! 




o 




c 


c 


w 


♦" 


to 


o 


H- 


«*- 




U- 




o 


o 


u 
o 


C 


— 


o 




o 




OJ 


XI 

c 


o 


0) 


1— 










o 


a 




§ 


c 


o 


in 









* 


^- 






cr. 


o 






»i— 


0> 


^ 




u. 










0> 


o 






o 


o 






o 

o 


> 






II 








o 


II 






o 








< 


> 







-130- 



and high-frequency components; thus, according to the preceding equations, A 

would be an unbiased (but noisy) estimate of A. Although V and X are relatively 

noise-free (The high-frequency components due to ey and e/\ are greatly atten- 

uated ), V could contain a small bias error introduced through ey, and hence, 

the error in X(= 1.) could accumulate slowly in time. 
P 

In an operational system, all vehicles would obtain position information 
from an absolute marker (e.g., a crossed wire or a magnet) at frequent intervals, 
and such errors, which are highly undesirable, would be reduced toward zero and 
have no long-term effect. In an experimental situation, in which the goal was 
to measure the response of an individual vehicle to various inputs, these 
errors could be large; however, if they were compared against a command signal 
generated onboard a vehicle (See Fig. 53), there would be little effect on 
the recorded responses (e.g., AV = V^ - V and AX = Xc - X), 

The signal -processor outputs are the inputs to the controller circuit 
shown in Fig. 54. This circuit is one realization of the controller design 
presented in the previous section. Here, sample-and-hold devices are used 
since X^., Vc, and Ac would only be available at discrete times if a digital- 
command generator were used (This would, of course, be the case in an opera- 
tional system). For this controller, no noticeable deterioration in system 
performance was observed if the sampling interval Tg were 0.1 sec or less. 
For Tg > 0.2 sec, the responses were under damped (or unstable), and the ride 
was generally uncomfortable. Thus, Tg was chosen to be 0.1 sec. 

The experimental procedure was as follows: At t = 0, the conmand 
trajectory shown in Fig. 55(a) was initiated, and as the vehicle responded, 
Vc» V, Xc - X, and V-j were recorded. This was repeated several times to verify 
that the response was consistent. 

-131- 




1. 
a; 



o 
u 



« 



3 



a. 

c 
o 






> 



in 






-132- 



ii 



lOOfl/sec 



ft/sec 




5 sec 



(a) Vc 




5 sec 



(b) X^-St 



Fig. 55 Full-scale response (X^. - x) 
maneuvering command. 



-133- 



A typical response {Xq - X) is shown in Fig. 55(b). Mote that the 
steady-state error was essentially zero during constant-speed operation, and 
was less than 0.5 ft when A^ = 2.0 ft/sec^. The responses at the midspeeds 
appeared to match the theoretical response (See Fig. 52(a)) fairly well. 
However, high-frequency (1 Hz) oscillations were present at low-speeds, and 
a relatively large overshoot was noticed at high speeds. If the model had 
been sufficiently accurate, this should not have occurred; thus, it appears 
that a more complex model is necessary. 

One such model, which is currently being studied, is shown in Fig. 45. 
A modified controller, based on this improved model, will be evaluated using 
the approach specified here (with the signal processor shown in Fig. 53). 
Eventually, the command generator (Appendix D)/ state estimator (Fig. 21)/ 
controller combination will be evaluated in complete full-scale tests in which 
the crossed-wires will provide an absolute position reference. 



-134- 



CHAPTER VII 
SUMMARY AND CONCLUSIONS 

A. Summary and Conclusions 

The achievement of safe and efficient longitudinal control is probably 
the most significant technical problem associated with individual automated- 
vehicle, transport systems such as the automatic highway and automated 
guideway transit. 

One general control structure would involve a central controller to 
oversee network operations with this including the coordination of sector- level 
computers — each of which would supervise and control the vehicles operating in 
its assigned sector. Four essential facets of operations at this sector level 

are: 

a) The specification and/or generation of vehicle 

command states; 

b) Communications between sector control and each 
controlled vehicle; 

c) The determination of the state of each vehicle; 
and 

d) The control of each individual vehicle. 

The research reported here was performed during the second year of a two-year 
study, and it deals with the design, development and testing of hardware systems 
essential for implementing these facets in the context of high-speed (to 93 
ft/sec), small time-headway (1-2 sec) operation. 



-135- 



The primary emphasis was focused on: 

1) The development of three prom-ising information 
source configurations for providing each vehicle 
in a sector with a continuous and accurate mea- 
sure of its state; 

2) The specification of realistic longitudinal con- 
trol systems which employ continuous (or near- 
continuous) inputs under both normal and emergency 
situations; and 

3) The demonstrating, under field conditions, of a 
vehicle control! er/information-source combination 
in various operational situations at speeds up to 
88 ft/sec. 

The secondary emphases were on: An examination of three general approaches to 
sector-computer operations; An overview of sector computer-to-control led vehicle 
communications; the identification of both the propulsion and braking dynamics 
of a typical U.S. sedan; and the evaluation of a fifth wheel as an information 
source. 

The first configuration for providing a controlled vehicle with state 
information involved the use of current-carrying conductors located, at 1-ft 
intervals, along a roadway. Signals from these conductors were detected and 
processed onboard a vehicle to obtain a discrete estimate of vehicle position, 
to an accuracy of better than ±.06 ft, as it passed each conductor. This 
could be achieved for conductor spacings from 1 to several hundred feet. A 
position interpolator with an equivalent accuracy was implemented to provide 
position information between conductors. However, the velocity estimates, 
derived from measurements of position of the wire crossings, were not 
a sufficiently accurate measure of a vehicle's "instantaneous" velocity. 

-136- 



The second configuration, which involves a vehicle's continuous acquisi- 
tion of position information, was comprised of two helically wound, transmission 
structures embedded in, or alongside, a roadway. The absolute position-measure- 
ment accuracy, per laboratory tests only, was 0.17 ft for "practical" line 
parameters — a result which is speed independent. Various approaches 
for obtaining a velocity estimate from these lines were considered. If P 
were small and a reasonable accuracy were present in the phase measure- 
ment, "instantaneous" velocity could be estimated to an accuracy of some 
0.9 ft/sec provided |A| < 3.22 ft/sec. 

The third configuration, a vehicle-borne radar and scattering 
enhancement plates embedded under the roadway surface, resulted in both 
an accurate position signal (e.g., a maximum position error of .05 ft in a 
10-ft distance) and an estimate of instantaneous velocity which is within 
±0.7 ft/sec of the true value of the speed range 0-100 ft/sec provided 
jA| < 3.22 ft/sec^ 

In essence, all three configurations, either singly or in combination, 

appear quite promising for use in a high-performance system. 

In many previous efforts on vehicle longitudinal control designs, 
simple linear models of vehicle dynamics were employed. Such models are not 
realistic for rubber-tired vehicles traveling at moderate to high speeds, and 
thus the designs presented were of limited value. Here, continuing the efforts 
of the first year, an empirical, nonlinear model of vehicle longitudinal dyna- 
mics was developed and employed in the design of a vehicle longitudinal control 
system. 

This system was demonstrated on a roadway where position information 
was obtained from embedded current-carrying conductors and an interpolator 
onboard the vehicle. The demonstration was successful in that a comfortable 
ride (|j| < 1.6 ft/sec^), an insensitivity to adverse environmental effects. 



-137- 



and fairly good position control (±2 ft tracking accuracy) were achieved. 
Superior performance, especially improved tracking accuracy, will be achieved 
in a modified design. 
B. Future Efforts 

Future efforts will be focused on the development of a complete 4 -mile 
sector wherein vehicles would be under the control of a roadside, sector-level 
computer. During the next year, this will involve the field installation of 
at least one of the three evaluated information sources, and the specification 
of the required computer and communications equipment. Subsequently, these 
items will be designed, implemented and installed in this sector so that 
complete sector-level operations may be achieved and evaluated under realistic 
normative and emergency conditions. 

When completed, this facility will provide a unique capability for the 
evaluation of most aspects of sector-level operations— information sources, 
vehicle controllers, computer hardware/software, etc. This will be an important 
step toward the demonstration of the technological feasibility of the automated 
highway. 



-138- 



APPENDIX A 

INSTRUMENTATION INSTALLED 
AT THE 
TRANSPORTATION RESEARCH CENTER OF OHIO 



In order to evaluate several realizations of an Information Source 1 
under field conditions, a small, instrumented test facility was required. A 
33O0-ft section of asphalt roadway, which is adjacent to the FHWA skid-calibration 
facility at the Transportation Research Center of Ohio (TRCO), was available 
for this purpose, and 2209 ft of this section were instrumented as shown in 
Fig. A-1. Approximately 500 ft of non instrumented contiguous roadway are 
always available for making a low-speed entry onto the instrumented roadway. 
When necessary, a high-speed entry can be obtained by using the figure "8" 
loop which is incorporated into the adjacent vehicle dynamics area. 

The completed installations consists of two separate units— a crossed-wire 
configuration and radar scattering-enhancement plates--which are sealed below 
the roadway surface. The former consists of 5 wires installed in the slots 
shown in Fig. A-2(a). Two wires each form a spatial square wave (See Fig. A-2 
(b)) which are located in the square slots along with two linear wires, and 
the fifth wire is located in the single linear slot. 

A crossed-wire configuration is obtained by exciting either (or both) 
of the square-wire configurations with an alternating current. As the lateral wires 
are 1— ft apart, the minimum marker interval is 1 ft; however, it should be clear 
that other intervals, which are multiples of 1 ft, could readily be obtained 
from this configuration. The single linear wire is used for an automatic 
steering reference; ultimately it, and the linear conductors in the square 
slots, will be evaluated for communications usage as well. 

-139- 




XJ 

o 

&. 

«♦- 
o 

c 
o 



u 
a 
</) 

-D 
0} 
♦-> 

C 

o; 

E 
3 
L. 
■♦-> 

C 



i 

<: 



05 



-140 



roadway center 



a) Slots cut into roadway surface (top view ) 



\ 

r 


— wire 


1 


f-- ~- - ~- — 


1 


1 


1 






1 
1 

t 

1 

1 

»l 




1 
1 

■ . 


' 


1 
■ 
I 
1 
1 
■ 

1 




1 
• 
1 
• 
1 
1 
1 
•_... — . — _ 


I 





z 



Wire 2 



b) Spatial square waves of wire 



Scattering enhancement 
plates 



Roadway surface „ 

2 —; 



\ ///// r ///////// / rr^ -^ 

h 21' H t 



c) Plates for use with Doppler Speedometer 



Fig. A-2 Installations under the roadway surface. 

-141- 



A 21 -ft section of scattering enhancement plates was installed as 
depicted in Fig. A-2(c). The plates were mounted in a vyooden structure (.167 ft 
X .167 ft X 21 ft) with ap = 30 , and positioned approximately 0.25 in below 
the surface. 

If it were necessary to evaluate helically wound transmission lines 
in a vertically-mounted configuration, then light wooden support structures 
would be installed at roadside. 

Other instrumentation was installed at TRCO under a previous contract. 
This consisted of two linear conductors, which were installed over a 3-mile 
distance in a precut slot between the 80 and 100 mph lanes on the 8-mile 
high-speed test track. Two miles are straight roadway, while the third con- 
sists of a transition and curve with a 2500-ft radius of curvature. This 
instrumentation was previously used in an intensive study of automatic steering.^' 



-142- 



APPENDIX R 
HELICAL TRANSMISSION LINES AS AN INFORMATION SOURCE 



A. Ideal Operation 

Two properly deployed helical transmission lines can be used to provide 
state information to ground vehicles. The operation of these lines may be 
understood by first considering the magnetic field H in the vicinity of a 
single line. Toward this end, consider the two parallel wires, excited by 
currents, I, shown in Fig. B-1. At the observation point 0. the components 
of H (Hx and Hy) are 

IV Iv 

and 



"y = 



Ux + h/2) _ I(x - h/2) ^g_2) 

Zirr-i^ 27Tr2^ 

where r^? = (x + h/2)2 + y2. r-^ = (x - h/2)2 + y2, and h, x, and y are defined 
in Fig. B-1.* In polar coordinates, the equivalent components are 

Hp = Hx cos <f> + H sin(j) 

H^ = -Hx sin <J> + Hy cos({). 



and 



These can be expressed as 



H = Ih sin 



Vn 



s d) + (h/2r)2j 



and 



4TTr2 Li +(h/r)cos * + (h/2r)2 1 -(h/r)cos (j) + (h/2r) 



Ha = L- r r ->-(h/2)cos (}> r - (h/2) cos <}) 

Ll +(h/r)cos d) + 



27rr2 Ll +(h/r)cos 4. + (h/2r)2 1 -(h/r)cos (() + (h/2r) 



+ (h/2r)2j 



* In order to comform to the conventional (r, 4», z) and (x, y, z) 
coordinate- system representation, z will be used for the longitudinal variable 
as opposed to x which was used in the text of the report. The text equations 
are obtained by replacing z by x and x by z. 

-143- 



If h/r « 1. then 



and 



. I h sin <^ 



. I h cos (j) 



so that 



H = -=^ [ sin d) r - cos * $]. 



(B-3) 



Here, r and $ are unit vectors as shown in Fig. B-1. 

Consider now the cross-sectional view of 4 parallel wires, excited by 
currents I] and I2, as shown in Fiq. B-2. The resultant magnetic field can be 
obtained by superimposing the fields of each line pair. The result is (for 
h/r « 1) 

H = " ■ [(I-| sin (}) - I2 cos <^)r - {l^ cos cf) + I2 sin (J))())]. 

If I] and I2 were the phasors 

I, = I„ ei" 



and 



I2 = lo e^J ^/2, 



loh 



then H would be 

H = -~5- [(sin (|) + j cos (\))r - (cos ± j sin ((>)(}>], 
Zirr'^ 

The upper sign corresponds to the + 90° shift on I2 and the lower to the -90° 

shift (This convention will be adhered to throughout this appendix). Since 



-•-*jc|> 



and 



H can be written as 



sin (|) + J cos (}) = +je 
cos <(> ± j sin (}) = e±J*, 

H = J2^ [Tjr- 4,] e±J*, 



(B-4) 



-144- 



^ 



* 



r.^ 



A 



II 



il 



I*- 



-H 



F1g, B-1 Two parallel v/lres with current I. 




O current out of poge 
® current into page 



Flq. B-2 Four parallel wires with currents I] and I2. 



-145- 



The expressions for the magnetic field of a helically wound line 
(of pitch length P), as a function of z, can be obtained as follows: Consider 
a cross-sectional view of the line at various positions along the z axis. The 
views would be rotated, relative to that of Fig. B-2, either in the clockwise 
direction for a left-hand pitch or counter clockwise for a right-hand pitch. 
Thus, if one assumes r « P, then 

H = Jo^ [Tjf - $] e±J> e?j(2Tr/P)z (e.5) 

2TTr'^ 

for a RH pitch. The corresponding expression for a LH pitch is identical if 
P is allowed to be negative. Here it was assumed that no phase change due to 

the propagation constant, 6, results. Thus, the frequency of excitation, f, 

27rf 
must be sufficiently low so that X » P, where X = —^ , and c^ is the velocity 

of propagation of the line. In rectangular coordinates, (B-5) is 

" = ^ f"'^ - y] ^*^'^* e»J(2''/P)z . (B-6) 

This form would be useful if Hj^ and/or H were detected. 

If a probe were positioned at a constant cross-sectional point (r = r^ 
and (|) = <\)q) and moved in the longitudinal direction, any component (H^, H^^, 
Hx or My) of the detected signal would undergo a continuous phase-shift — totaling 
360°for every P distance moved. For motion in a given direction (±z), this 
phase shift would be positive or negative depending on the method of excitation 
and/or the sense of the pitch. 

A reference must be available to measure phase. This could be obtained 
from another hen'cally-wound line.* A proposed configuration is shown in Fig. 
B-3, where arbitrary pitches P-\ and P2 are shown. The method of line excitation 



* Actually, any transmission line could be used. The superior noise- 
rejection capability of the helical structure makes it a strong candidate. 
In addition, if similar structures are used for both lines then any effect of 
B on the phase difference (however slight) would cancel. 

-146- 



<D 



N 





CD 




1 1 


— 


1 


E 


PHASE 
ETER 


Q 




±j 



CM 

o 



+♦ 



o 

II 

























Q- 

< 




CL 
< 




CL 
< 




a. 
< 




1 




1 


1 






1 




i 


1 


o 








o 


O 
CD 

4-1 








O 
■i-i 




i 








. 






i 

cr 

LU 

z 

LiJ 






















C 
O 






I/) 

c 
<o 

1. 



"O 

c 

o 

5 






o 

3 

cr. 

c 

•r- 

3 

E 
0) 

4-> 
(/) 

>, 
(/) 

0) 

u 

c 

i~ 
o 
**- 

I. 



to 

c 

■5 



cr. 

c 
o 



o 

c 
o 



I 

as 



cr 



-147- 






t- 




o 




**~ 


CM 


c 
o 




•^- 


— a> 


4J. 


\E 


<0 
4-> 


iM^ 


•^" 




U 




X 




0) 




■D 




c 




<o 




• 




c 




o 




•^• 




<*-> 




to 




u 




o • 




r- n 




1 




0) 00 




^ 


D 


O a; 




t. t. 




C 3 




CT- 




• '^ 




1^ 




•♦-> C 




«/) •»- 




>. 




(/) c 








0) o 




♦J x: 




«3 CO 




c 








■5 o) 




U 4-> 




O i/> 




O >. 




O 1/) 


— 




-0) 


1 


c 


CO 



-148- 



and probe placement is shown in Fig. B-4. The probe spacing, d, was chosen to 
equal the line spacing, and the probes are assumed to measure Hy (The results 
would be similar if H^ were measured). 

Using (B-6) for Lines 1 and 2, the phase difference as measured by a 
phase meter would be 

e^jjCz) = arg (Hy2) - arg (Hyi). 

This reduces to 

ed+ (z) = 2(({>2 - (t)^) - 2ttz(J- - J-) (B-7) 

for a choice of +90'' for I2 on both lines, and 

({.d_(z) = 2((|)2 + (|)l) - 2ttz (J- + J.) (B-8) 

for a choice of +90° for I2 on Line 2 and -90° on Line 1. 

In each of the preceeding equations, the phase difference is a spatially 
periodic function of z, and a typical v/aveform is shown in Fig. B-5. Here, 
pQt the "effective pitch length", is given by 



1 - 1 _ 1 



(B.9) 



Pe P2 Pi 

Any desired value of Pe (both positive and negative) can be achieved via the 
selection of P] and P2. 

9d(z) 
+ I80**i 




Fig. B-5 Theoretical phase-difference versus the longitudinal coordinate, 

-149- 



Thus, the longitudinal position of a vehicle could be determined if it 
were equipped with appropriate probes and a phase meter. For absolute position 
measurement, a counter would be needed to indicate the number of 360° phase 
traversals made by the signal. This would be a "coarse indication" of position. 
The measured phase within a period of the waveform would be a "fine indication" 
of position. 

Additional versatility, which may be useful, would result if the two 

lines were operated at slightly different frequencies. If f] = fg and f2 = 

fo + Af, and the frequency difference were viewed as a time-changing phase 

shift a = Awt, then (B-6) would contain an extra factor of e'''^^'*'* for Line 2. 

Then (B-7) and (B-8) would become 

ed+(z. t) = 2((f)2 - A] ) - —^ + Aiot 

'^e 
and « 

ed-(z. t)= 2(<1>2 + ^l) - ~^+ ^t- 

Pe 

The waveform would still be periodic in z, but the wave would move at a velocity 

V|^. This can be found by setting de^/dt = 0, with the result 

Vh = PeAf. (B-10) 

B. Deviations From Ideal Operation 

In the implementation of this configuration (see Fig. B-3), the measured 
phase will deviate from the theoretical value for two reasons: First, since 
the field equations were derived on the basis of four-parallel wires, devia- 
tions will occur if P is not greater than r. Second, since each line and its 
probe cannot be entirely isolated from the other pair, deviations due to cross- 
coupling will occur. These factors would cause a simple bias on the phase if 
the probes were maintained at a constant cross-sectional point (r = const. 



-150- 



<() = const) during longitudinal travel. However, due to the expected lateral 
and vertical motions of the vehicle, deviations in the measured phase would 
occur and be interperted as erroneous longitudinal position changes. 

The effect of a finite pitch length is difficult to treat analytically. 
However, from the numerous laboratory experiments conducted, it was surmised 
that for Pi>2ftand P2 >2f t, the corresponding phase-errors, should be 
inconsequential. 

The effect due to cross coupling was treated both analytically and 
experimentally. In both cases, parallel wires (infinite pitch length) were 
used so that the effects could be isolated from the pitch-length factor. 

Consider the configuration of Fig. B-6 wherein the probes are shown 
at positions (x = Ax, y = yo + Ay) deviating from the desired positions (x = 
^» y - yo). The magnetic field detected by Probe 1 would be 



27r 



2Tr 



H 



yi 



and that by Probe 2 



loL e^^"2^1 e^J ?7 ^ i£ll e-^'^*l \'^ k " 



2Trr 



27ra2 



_, 2tt 



-,• 27r 



y2 






27rr2 2TTr2 

Here c})], (}>^ ' , ^2* ^2'» ^» ^"^ ^ ^''^^ defined in the figure. The leading term 
in both equations is the ideal signal. The second term is the undesired 
signal. 

After rearrangement of terms, there results 



_, 2tt 



and 



yi 



>2 



loh ±j2(f,i Tj B. z ^^ ±j<Sl 



2TTr2 



e p, m-je 



" *» e Pj> m2e 



27rr2 



(B-11) 



(B-12) 



-151- 



M 



o 



O 




Z3-» 



c 
o 



u 

o 



•a 



£ 

O 
1. 



C 
10 

< 
a; 



(/> 

c 
o 



<o 
u 
o 



o 

01 



1. 
o 

>. 
1. 
■«-> 

O) 

E 

o 

CD 



I 

CO 



en 



-152- 



where 
and 



m e-^^"^l = 1 + ''^ e-^^^'^l' ^ 2(})i ?(27r/P2) z ±(27r/Pi)z) 



m2e 



j'^2 - 1 + r2 ±J(2c})2' ? 2({.2 + (27t/Pi) z ±(27t/P2)z) 



{B-13) 

(B-14) 



Equations (B-7) and (B-8) become 



,1 1 



and 



Od. = -27TZ (^--r-) + 2(62 - (f)]) + (62 - 61) 
+ ^2 ^1 

ed_ = -2ttz (~ + ^) + 2((})2 + c()i) + (62 + 61) 



(B-15) 
(B-16) 



The leading term 1n each equation is the theoretically desired one while the 
last two terms represent phase-errors. 

An obvious means of reducing the phase-error is to use the excitation* 
which yields 6^+. For simple vertical and lateral vehicle motions with no tilt, 
(})1 = (^2 ^^^ ^^^ phase-error (ee) would be 

ee = 62 - 6t. (B-17) 

From an examination of (B-13) and (B-14), it is apparent that 61 and 62 are 
phase angles which result from the addition of two phasors — one of which is 
unity and a second a small phasor of arbitrary angle as shown in Fig. B-7. 
If r2/a2 « 1, then the maximum value of 61 will occur when the phasor repre- 
senting r2/a2 is at a 90° angle; then fi-i^ = sin-1 r2/a2. A similar argument 
yields 62m = sin'^ r^/b^. Since, in general, the two angles could be equal 
but of opposite sign, then 

eg < sin-"" r2/a2 + sin-l r2/b2. (8-18) 

where from the geometry of Fig. B-6, 



* To use this mode, one must insist that P] f ?2 so that Pq is finite. 
Either non-equal pitches of the same sense or arbitrary (equal or nonequal) 
pitches of opposite sense would suffice. Thus, any value of Pg could still be 
achieved— at least in theory. 

-153- 



I imaginary 




real 



and 



Fig. B-7 Phase angle fi-j which results from the addition of two phasors, 

r2 = (y + Ay)2 + (ax)^, 

a2 = (d - Ax)2 + (yo + Ay)2 

b2 = (d + Ax)2 + (yo + Ay)2 



C. Experimental Verification 

The theory of a helical-line information source, as developed here, is 
based on (B-6), Note from this equation that H^ and Hy have a similar form; 
therefore, an experimental measurement of one component (Hy) should suffice to 
validate the theory. 

First, Hy vs. r was measured for single lines of various diameters 
(1/4, 1/2, and 1 in). The results are shown in Fig. B-8 for Iph = 0.5 (The 
units are peak-to-peak amperes x inches) together with the theoretical l/r^ varia- 
tion. Within reasonable limits, the signal from the lines varies as l/r^. 



-154- 



1/2" core 




„ —^ variation 

r2 



r (Inches) 



12 13 l^ 15 16 17 18 



Fig. B-8 Amplitude of Hy versus distance from the line. (loh = 0.5). 

-155- 



Second, the variation 1n the phase of Hy, as the probe was moved over 
a wide cross-sectional region, was measured (The coordinates are defined in 
Fig. B-2). The results for the 1" diameter line are shown in Fig. B-9 and 
the theoretical results in Fig. B-10. (The results for the other lines were 
similar and are not presented here). Note the generally close agreement bet- 
ween the two; however some distortion exists on one side of the line.* It 
was concluded that an accurate model for line behavior has been developed. 

Lastly, a detailed study of the phase-errors which would be incurred 
due to lateral and vertical motions of the vehicle was conducted to verify 
(B-17) and (B-18). Three different line sizes v/ere used but only the results 
from the 1/2 in. diameter line are shown for brevity. These are shown in 
Fig. B-11 and the theoretical results, per (B-13), (B-14) and (B-17) are shown 
in Fig. B-12. A reasonable agreement exists for y £ 15 in., and these equations 
may be used with confidence in the design process. 

An upper bound on 9e» which was given by (B-18), is plotted in Fig. B-13. 
While this deviates considerably from both the measured and theoretical results, 
it provides a very conservative but easily calculated estimate. Thus, this 
upper bound was employed in the calculations of Chapter IV. 

VJhile the tests reported were conducted using 30 in. line separations, 
the results indicate that calculated values for other separations should be 
satisfactory for design purposes. 



* This distortion was due to the presence of steel -reinforcing 
material which was placed under the lines for all tests. This material 
also caused the asymmetry of the phase-error curves of Fig. B -11. All 
results given in this appendix include the effects of reinforcing material 
and are thereby more realistic than those that could have been obtained 
without it. 

-156- 




bH 



XOnches) 



i^ 



F1fl. B-9 Variation in the phase of Hy for various positions in 
the cross-sectional plane. (Experimental results). 

-157- 













110 1 


(deg) 


y 












100 ■ 


- 




/ 












90 ■ 


■ 




y 












80 ■ 






/ 












70 


















60 






^y^ 












50 ■ 






yy' 












40 






y^ 












30- 






/^-^ 












20 






,-^^ 












10 ■ 








6 


5 


4 


3 


2 


1 




2 3 4 


5 6 










^^^ 




•-I0 




X (inch( 


^-^^ 


-^ 


"^ 


-;;/ 


# 




-20 






y=19'>- 


^^ 


/;; 


</ 


V/ 




-30 


r'sq.core 




y=i4>- 


-^ 


</ 


/y 






-40 


Io=0.5 A p-p 




y= 12'!^ 


y 


X y 


/ 






-50 






y=IO'>" 


/ 


^ / 


^ 






-60 






y = 8>/ 


/ 


> 


/ 






-70 
-80 






y=6V 


/^ 


/ 








-90 






y=4" 


/ 


f 








-100 

-no 







Fiq. B-in Variation in the phase of Hy for various positions in the 
cross-sectional plane. (Theoretical results). 

-158- 



35 




25- 



20.. 




X(inches) 



-6 -5 -4 -3 -2 -I 



-5 ■ 



GgCdeg) 



1/2 sq. core 
lo =2Ap-p 

d = 30in. 



y=l5 



Fiq. B-ll Phase-error (Gg) for various positions of the 

probes in the cross-sectional plane. (Fxperimental 
results.) 

-159- 



/2"sq. core 




Fin. B-12 Phase-error (e^) for various positions of the nrobes in 
the cross-sectional plane. (Theoretical Results). 

-160- 



1/2" sq. core 



y = l5 




-6 -5 -4 -3 -2 -I 



I 2 3 4 5 6 X (Inches) 



Fig. B-13 An upper bound on the phase error (Gg) for various positions 
of the probes in the cross-sectional plane. 

-161- 



APPENDIX C 
ON THE IDENTIFICATION 
OF 
BRAKING DYNAMICS 



A. A Model of Braking/Roadway Interface Dynamics 

Braking dynamics are generally represented by 

V = -^Vi (p=^) (C-1) 

where 

V is vehicle speed, 

V^- is the input to the braking system, 

Ke is a fixed gain, and 

T is the braking system time delay. 
The primary advantage of this model is its simplicity; hov/ever, it results in 
a poor approximation of the behavior of a braking vehicle in many practical 
situations, and its use could result in unrealistic performance predictions. 
This would be highly undesirable in view of the exacting braking requirements 
which would be imposed on an automated ground vehicle operating in a high-speed, 
small time-headv^ay environment. 

The relationship between V and M\ would be dependent on such factors 
as the condition of the brakes, the properties of the tire/ road interface, and 
a vehicle's deceleration rate (A). This relationship v/ould be nonlinear and 
probably quite complex. As the goal of the effort reported here is the design 
of a closed-loop braking system, it is probably not necessary to employ such a 
complex form, and a much simpler one, involving an input-output relationship 
for an expected range of vehicle speeds and deceleration rates, could be 

-162- 



adequate. This model would be a nonlinear differential equation whose para- 
meters were dependent on V, A and V^. A further simplification would result 
if it were assumed that nearly linear operation were obtained for a prescribed 
set of conditions (i.e., a fixed command deceleration rate from an initial 
speed (Vq). Then 

p"V = g[p"-'' v.... A. V. Vil, (C-2) 

where q defines a linear relationship among the variables in its argument. 
This relationship would contain quantities which changed with condition, thus 
partially accounting for the nonlinearities in the braking dynamics. A dis- 
advantage of this approach, which was the one adopted here, would be the failure 
of a specified model to predict some critical events (e.g., the onset of wheel 
lock). 

It was hypothesized that the bra king/ roadway interface dynamics of a 
typical U.S. passenger sedan could be represented, at least for the purpose 
of designing a closed-loop braking system, by the model shown in Fig. C-1. 
This model contains 5 quantities Kg, a, B, 6, and t, which were assumed to be 
dependent on both Vq and A^, and its form was specified after an examination 
of data obtained from braking tests. 



Vi 


KBe-*P{p+/) 

p(p+o<) (p + /i) 


V 







Fig. C-1 A simple model of braking/roadway-interface 
dynamics. 

-163- 



D. Identification of Model Parameters 

One approach toward obtaining the model parameters is via open-loop 
testing. This would involve driving a test vehicle at a fixed speed Vq, 
applying a braking command (A^)^ obtaining the resultant response, and then 
estimating the parameters corresponding to Vq and A^.. Unfortunately, this 
approach is of limited value because of the inevitable presence of both small 
unwanted disturbances and higher-order effects (not considered here) which 
result in highly inconsistent and nonrepeatable results.^' However, this 
approach could be, and was, employed to obtain a value of some 150 m sec for 
T— a value which was somewhat independent of both V^ and A^. 

More consistent results may be obtained by using a closed-loop configu- 
ration, and this approach was adopted here. The quantities Kg, 5, a and B were 
specified via a model -matching technique in which the response of the closed- 
loop model, shov/n in Fig. C-2, v/as matched to that obtained from a corresponding 
full-scale implementation. The model input is the command velocity (V^,), the 
braking system input is V^**, and the output is V. 

The compensator (Gj.) should be selected so that low-error performance 
(e.g., AV = Vq - y^ small) is obtained, as this would be a requirement on a 
system intended for operation in a high-speed, small time-headway environment. 
Several compensators were evaluated including two proportional-plus-integral 
units and a gain-only unit; here only the latter with 

G(. = 1.0 
was employed in the identification process. 



* In a full-scale situation, M^ would he the voltage input to an 
electrohydraulic actuator which would control brakeline pressure. 

-164- 



Vr 



-.AV 


Gc 


Yi 


Vehicle 


V 


J • 




or 






_• 

1 






Model 















Fig. C-2 Closed- loop system employed in the 
parameter-identification process. 



The model parameters were obtained via the follovn'nq procedure: 
The large-signal command Input 

Vc = Vo - Act [0. ts] 
was applied to a test vehicle which was traveling at a 
fixed speed Vq on a nearly level, concrete pavement and 
the signal AV was recorded. Here t = Is the time the 
brakes were applied, and ts Is the time the vehicle speed 
was zero. This procedure was applied for both dry- road 
and wet-road conditions. For the former, tests were 
conducted for each of five speeds (20, 40, 60, 80 and 90 ft/ 
sec) and four deceleration (6.44, 9.66, 12.88, and 14.5 
ft/sec2) combinations, while In the latter tests were 
conducted for each of five speeds (20, 40, 60, 80 and 90 
ft/sec) and three deceleration (6.44, 9.66, and 12.88 ft/ 
sec2) combinations. Here, running water to a depth of 

L- - i In was present on the surface of the concrete road- 
16 8 

way. This condition resulted in a very unfavorable 

environment for effective braking action. 

-165- 



(C-3) 



The full-scale conditions were subsequently replicated 
in the laboratory. The closed- loop model was excited with 
an input (Eqn. (C-3) and AV was recorded. This was matched 
with the AV obtained in the corresponding full-scale test 
by appropriately adjusting Kg, a, B and 5. Thus, these 
quantities were assigned values for each speed-deceleration 
condition.* 

C. Experimental Apparatus 

A 1969 Plymouth sedan v/as employed for the full-scale testing. The 
braking and accelerating functions were accomplished via electrohydraulic 
control systems and the actuator, which controlled the brake-line pressure, 
was characterized by a corner frequency of some 7 rad/sec. This vehicle had 
drum brakes with the two front and two rear brakes independently operated 
via a dual-master cylinder. 

A computer, consisting of 20 operational amplifiers, 18 potentiometers, 
and other necessary components was installed over the back seat. The computing 
elements were used for system compensation and data collection. All data 
collected were recorded on a six-channel, strip-chart recorder located next 
to the driving position. In some tests, vehicle speed was measured via a 
calibrated tachometer connected to the drive shaft. The resulting signal was 
denoted by Vj and thus, in these cases, V = Vj and AV = V^ - Vj. In all other 
tests, V was obtained via a fifth wheel whose measured output was denoted by 
V5. Then, V = V5 and AV = Vc = V5.** 

* The time delay was neglected in this identification procedure. 

** Both of these approaches result in an approximate value of V; however, 
in view of the 5th wheel data presented in Chap IV, and some braking data 
reported in this chapter, this approximation seems reasonable. 

-166- 



All testing was conducted on the linear section of the skid pad at the 
Transportation Research Center of Ohio. The grading of this 8000-ft section 
varied from .44^^ at one end to -.50% at the other. 
D. Experimental Results— Dry- Pavement Conditions 

Typical full-scale and model responses (aV vs. t) for dry pavement 
conditions, Ac = 6.44 ft/sec^ and Vq = 20, 60 and 90 ft/sec are shown in Figs. 
C-3(a), (b) and (c), respectively, and similar responses for Ac=14.5 ft/sec^ 
are shown in Figs. C-4(a), (b) and (c).* In these cases, V = Vj and AV = Vc - 

Vt. 

The following should be noted from an examination of the full-scale 
responses: 

1) The response changes with V^ie.g., the time at 
which the peak value (AVp,) occurs increases with 
increasing Vq); 

2) The magnitude of the response does not increase 
linearly with increasing Ac (e.g., for Vq = 90 ft/ 



AV 



m 



AV 



m 



sec, -J— = 0.81 for A.c=6.44ft/sec2 while ~ 
= 0.45 for Ac - 14.5 ft/sec^); and 
3) The form of the response changes with Vq and/or 
Ac. 
In essence, the braking dynamics are a nonlinear function of at least V^ and 
Ac, and this property must be explicit in the specified model. 

Additional full-scale data, which were collected on a different day than 
that presented above, are shown in Fig. C-5 for V^ = 20, 60, and 90 ft/sec and 
A^ = 14.5 ft/sec^. The responses on the left were obtained for V = Vj while 

* The full-scale responses presented in this chapter were copied from 
the original records so that these responses could easily be compared with those 
from a model. 

-167- 



5- 
AV - 
(f/s) - 



— Full-scale response 
" Model predictions 



"I r 



T 
5 



T 1 r— 

Time (sec) 







a) Vq = 20 ft/sec. 








T 
5 



T 1 r- 

Tinne(sec) 



■T r 



10 



[)) Vq = fin ft/sec. 




c) Vq = 90 ft/sec. 



F1g. r-3 Comparison of vphicle response and model 
response for 3 selected initial speeds 
and Ac = 6.44 ft/sec2 (Dry-pavement conditions) 



-168- 




— Full-scale result 
X Model predictions 



"" r 

5 



T ' r~ 

10 



Time (sec) 



a) Vq = 2n ft/sec. 




—I r — -" — I 1 1 ' 1 1 — 

5 Time (sec) 10 

b) Vq = 60 ft/sec. 




c) Vq = 90 ft/sec. 



Fig. C-4 Comparison of vehicle response and model 
response for 3 selected initial speeds 
and Aj. = 14.5 ft/sec2 (Dry-pavement conditions). 

-169- 




u 



c 




-lO 



> 

II 
> 




- lO 






II '-» 




«/i 




> c 




o 




l-«l- 




o •«-> 




M-«r- 




•a 




a; c • 




U) o --^ 




C U 0) 




o cr, 




a.*J « 




(0 c o. 




0^ o 








r- > •»- 




OJ ro 2 




T3 O. O 




O 1 r- 




E >,»- 


• 


i. O 


u 


T3 -O «♦- 


<u 


C 


1/) 


«0 XJ OJ 




C f 


4J 


0) <o •♦-> 


<|- 


iA 




CCM C 


o 


o o o 


KC 


Q. a; 




«/>»/) -c 


II 


a; -^ a; 


1- ■!-» c 


o 


«♦- 'r- 


>. 


Q) <0 




f— LO 4J 




(J • C 


^.^ 


•t- -a- o 


x; 


x: r- o 




& 




> II to 




•^" 




H- O 




O < '— 




*-^ o 




c in — 




o >• m 




(/) 1 




•r- II o 




i- 




«o > • 




Q- cr- 




E X3 -r- 




o c u. 




o <o 




ID 




1 




o 



-170- 



0) 




CO 




c 




o 


<D 


Q. 


</) 


U) 


c. 


<D 


o 


^ 


Q. 




cn 


0) 


(i> 




w 


o 




o 


___ 


(O 


0) 




-o 


3 


o 


Ll. 


s 




u 



0^ 



U 



o 


c 




M- 


O) 




OJ 


Q^ 




U) 


> 




c 


«c 




o 


Q. 




a. 


1 




to 


>^ 




O) 


L. 




u 


-o 




,_ 


T3 




a; 


C 




■o 


(O 




o 






ECsJ 






u 




X3 


a; 




c 


1/) 




<TJ 


4-> 




a; «♦- 




in 






c 


IT) 




o 


• 




c^ 




w 


fMM 




OJ 






L. 


II 




o; 


u 




^- 


•a: 




o 


^— ' 




•f— 






x: 


ID 




Ol 


> 




> 


II 




<♦- 






o > 


• 


c 


"O 


V) 


o 


c 


c 


to 


lO 


o 


•^ 




•r- 


L. 


1— 


■M 


TO > 


•r- 


Q. 




TD 


E 


II 


C 


o 




o 


o 


5> 


u 


U) 






i 






o 







o 



> ^ 



-171- 



those on the right were obtained for V = V5. Compare those of the left with 
those presented in Fig. C-4, which were obtained under identical conditions. 
The shapes of the corresponding curves are the same for each coirmon speed; 
however, the maximum amplitudes differ (e.g., A\f - 7 ft/sec in Fig. C-4(b) 
vs. AVfn = 8.5 ft/sec in Fig. C-5(b). These differences are typical of the 
variability which was observed in all of the collected data. 

Given this variability, a model cannot be specified that will precisely 
match all of the observed responses for a given condition, and an approximation 
must be employed. Thus, the model for each Vq - A^. condition was selected so 
as to be consistent with the median magnitude response (as obtained from 5 
trials conducted on different days over a 3-month period) for that condition. 
It is these model responses which are superimposed on the full-scale (median 
magnitude) responses of Fig. C-4 and those of Fig. C-5. Mote that the corre- 
lation between the model -and full-scale responses is much better in the former 
than the latter. 

The composite model is presented in Table C-I where Kp, a. P., and 5 are 
specified for various V^ - A^. combinations. The change in model parameters as 
a function of both Vq and A^. is shown in Fig. C-6 where the quantity -^ is 
plotted versus V^ with A^. as a parameter. If the model ^'le.re linear, this 
quantity v/ould be invariant with respect to both of these quantities; instead 
it varies over a ranne from 2.63 to 1.25. 

The variability in performance can be accounted for by specifyinn a 
range of Kg for a given Vq - A^, combination. Correspondingly, one would have 

a range on ^ ' such as is shown by the dashed lines in Fia. r-6. I'hese 

aP 

correspond to observed changes in Kg of some ±20X, which encompasses the range 
observed from the collected data. 

-172- 

















1-^ 










^— ^ 


en 


*— » 


r*^ 


— -Iro 




ro 






in 


+ 


in 


+ 


in 


+ 




+ 






• 


Q. 


• 


c 


• 


o. 


*—>«, 


o. 






+ 


*— - 


+ 


*^^^ 


+ 


•»»-<' 


m 








o. 


»— ^ 


Q- 


■— ^ 


ex. 


<»-v 


• 


«*«^ 




O 


»— ^ 


in 


— u^ 




un 


+ 


LO 




a^ 


in 


»• 


in 


• 


in 


• 


o. 


• 






Csj 


^— 


^— 


r— 


"^ 


F— 


"^.^ 


r* 






• 


+ 


• 


•«- 


• 


+ 


m 


-♦■ 






r— 


Q. 


C\J 


CL 


ro 


o. 


r— 


o. 








C- 


" 


O. 




Q. 




"a. 








,_^ 




„^ 




■ ^ 




^_^ 






*— «» 


ro 


^^ 


ro 


,— .. 


ro 




no 






in 


+ 


in 


+ 


in 


+ 




+ 






• 


o. 


• 


Q. 


• 


a. 




o. 






+ 


■^^ 


+ 


•w^ 


+ 




in 








Q. 


^■^ 


Cl. 


^^ 


Q. 


»-*-s 


• 


.«*^ 




o 


««_^ 


in 


V—' 


in 




m 


•t- ko 




00 


in 


• 


in 


• 


in 


• 


a. 


• 






CO 


^- 


^ 


r— 


•0- 


w 




p> 






• 


+ 


• 


+ 


« 


+ 


in 


+ 






^- 


Q. 


CVJ 


Cl 


ro 


o. 


f— > 


o. 








cl 




O. 




"a. 




o. 








_^ 




,_^ 




^^ 










in 




m 




in 










• 




• 




• 








^— N 


ro 


*— » 


ro 




ro 


^— > 








^- 


+ 


^ 


+ 


4«— >. 


+ 


in 


•— X 






+ 


c 


+ 


c 


r^ 


c 


r^ 


«i^ 




o 


o. 


"w' 


c 


>_^ 


+ 




• 


+ 




vo 


^— ' 


"— <. 


V— ' 


■— >. 


D. 


-~» 


r— 


C- 






rv. 


in 


^1- 


in 


«.»<' 


X) 


+ 








in 


• 


ro. 


• 


^ 


• 


^^ 






• 


C\J 


• 


CVJ 


• 


CM 




ro 






in 


+ 


«:r 


+ 


VO 


+ 


CO 


+ 






r— 


Q- 


r— 


c 


r— 


cr 


• 


Cl 








^-^ 




^^^ 




k^ 


«a- 










C 




a. 




Cl 




"c. 






^^ 


■ 












in 




in 


,».« 


,— ^ 


,— ^ 


^-«» 






r*>. 


<— % 


r*. 


"S- 


in 


«d- 


in 


,— ^ 






# 


«* 


• 


+ 


r*. 


+ 


t^ 


^3- 






^^ 


+ 


^— 


ex 


• 


CJ. 


• 


+ 






+ 


O- 


+ 


^.^ 


p— . 




•"" 


Q. 




o 


CI 




Q- 


— * 


+ 


•— ^ 


+ 






«3- 


<«-^ 


•— V 


«_^ 


ro 


a. 


ro 


o. 


>-^ 






o 


ro 


CM 


+ 




+ 


v_^ 


ro 






+ 


CO 


c 


in 


c 


in 


+ 






U3 


Ol 


• 


.ta^ 


• 


-^^^ 


• 


Q. 






•«««^ 


ro 


c 


m 


a. 


in 






\ 




Q. 


•" 




•" 




^ 


O. 






^_^ 




^_^ 




^ 












in 


r~^ 


in 


^o 


in 


»— * 


in 


»-««, 






1-^ 


«^^ 


r* 


^ 


r-o 


^ 


r-. 


^ 






• 


+ 


• 


+ 


• 


+ 


• 


+ 






r— 


Q. 


^ 


o. 


r- 


c 


^- 


CL 






+ 


h«.^ 


+ 


*— <• 


+ 


^^^^ 


+ 


■ta..^ 




o 


C 


^—^ 


c 


.»— .. 


c 


'-^ 


a. 


^^ 




CM 


^^^ 


ro 


^-^ 


CO 


^^•' 


ro 




ro 






in 


+ 


in 


+ 


in 


+ 


in 


+ 






•a- 


o. 


^ 


c 


«* 


c 


•a- 


Q. 






o 


k_' 


o 


S.' 


c 


ta_^ 


o 








• 


o. 


■ 


G. 


« 


o. 


• 


loi 






00 




00 




00 




00 








•" 




*" 




'^ 




•^ 




^_^ 












u 












o; 












O (/) 












> >«^ 












4-* 












«•- 












^— ' 




^ 


XO 


00 


o 






^ 


iO 


00 


ir> 






• 


• 


• 


• 




/ ^"^ 


vo 


04 


CVJ 


^ 




/ cvj 






#"^ 


^^ 




r o 










/ 


a> 










/ 


o W> 










/ 


<: ^^ 










/ 


•*-» 










/ 


«4- 










/ 





















c 
o 



o 
u 



u 
o 






o 

LO 






UJ 

o 







.00. 






+ 




^^^ 






«o 


c 




+ 


o" 




CL 






^-^ 


+ 




ca 






i-ti 


o. 


•-H 


91 


1 




o 


=?ls: 




LU 




-J 


oc 


CO 


o 


<: 


u. 



in 



LU 
CL. 



o 
o 



-173- 



Kb£ 



3.0i 
2,0 

l.o^ 









Xoo-i- 



20 



JP 



a 

s 



A^Cf/s^) 

6.44 

9.66 

12.88 

14.5 



+ 



40 60 

Vo(f/s) 



80 



100 



1/ t 
Fig. C-6 — g. vs. Vq with A^ as a parameter. 

Next compare the responses on the left-hand side of Fie. C-5 with the 
corresponding responses on the right. In each case (e.g., Vq = 40 ft/sec), 
the responses are approximately the same differing only in the greater amount 
of noise present when V = V5 (The primary source of this noise was the bouncing 
of the 5th wheel).* In view of the similarities here, as v^ell in other collected 
data, it was concluded that Vj = V5 under dry-pavement conditions, and thus the 
same model could be employed for the two cases. 

The magnitude of G^ cannot be too large or the model is not valid-- 
especially under high-speed conditions. Thus, when G^ = 2 and tests were con- 
ducted at a moderate initial speed (e.g., Vq = 60 ft/sec) and A^ = 14.5 ft/sec^. 



* This noise was not included in the redrawn full-scale responses of 
Fia. C-5. 

-174- 



the model and full-scale responses are generally consistent as is shown in 
Fiq. C-7. However, when tests were conducted at higher speeds (Vq = 80 ft/sec) 
and Ac = 14.5 ft/sec^, good correlation was not obtained as wheel lock occurred 
as shown in Fig. C-8. The closed-loop system then responded in an anti-skid 
mode and thus prevented the loss of vehicle lateral control. The resulting 
response was highly oscillatory and a wery jerky ride resulted. It appears 
clear that high gains, and corresponding small errors in the controlled var- 
iable, should only be employed in conjunction with a more effective anti-skid 
system than was employed here.* 
E. Experimental Results— Wet Pavement 

Typical full-scale and model responses (AV vs. t) for v/et-pavement con- 
ditions. Ac = 6.44 ft/sec2, Vq = 20, 60 and 90 ft/sec, and V = Vj are shown in Fig. 
C-9. The model responses are those obtained from the parameters specified in 
Table C-I. As good correlation exists between these responses, it was concluded 
that the model specified for Ac = 6.44 ft/sec^ was also adequate for the wet- 
pavement case. This is also true for Ac = 9.66 ft/sec^; however not for Ac 
>^ 12.88 ft/sec^ and V = Vj. This may be seen in Fig. C-10 where AV vs. t 
is plotted for two cases— Vq = 20 ft/sec and Vq = 40 ft/sec. In the former, 
good agreement exists between the model and the full-scale result whereas in 
the latter, the correlation is poor. Wheel lock occurred, and the braking 
system responded in an antiskid mode. The resulting response was, as shown, 
highly oscillatory, and quite different from the predicted response. However, 
if a more efficient anti-skid mode (one that would have resulted in minimal 
amplitude oscillations and a more comfortable stop) had been employed, the 
model response would have been a fair approximation of the full-scale response. 



* If such a system were employed, then the model response would be a 
good approximation to the full-scale response as is subsequently discussed. 



-175- 




Full-scale response 
Model response 



1 1 1 p 

Time (sec) 10 



Fig, C-7 Comparison of vehicle and model responses for 

a hiqh-gain control confinuration (Vq = 60 ft/sec, 
Ac = 14.5 ft/sec^, 0^ = 2.0 and dry pavement). 



sec 




Fiq, C-8 Vehicle response under anti-skid conditions 
(Vq = BO ft/sec, Ac = 14.5 ft/sec2, Gc « 2 
and dry pavement). 



-176- 




Full-scale reponse 

*f Model predictions 



— -1 1 1 1 1 1 1 

5 Time (sec) 



T r 



10 



a) Vo = 20 f/s. 




b) Vq = 60 f/s. 




1 1 r 

5 Time(sec) 



X 



//. 



-rrrr 



9 12 



c) \'o = 90 f/s. 



Fig. C-9 Comparison of vehicle response and model response 
for 3 selected initial speeds and f^r = 6.44 f/s'^ 



(l.'et- pavement conditions and \/ = \'j 



■I 



-177- 



Thus, if the large oscillations of Fig. C-lO(b) were greatly reduced, the res- 
ponse shown In Fig. C-11 would result. This response compared favorably with 
the model response which Is also shown. 

Essentially the same results were obtained when V = V5 the main differ- 
ence being a smaller magnitude response for Vq >. 40 ft/sec (such as could be 
caused by a slight Increase in Kg). This 1s illustrated in Fig. C-12 where 
full-scale and model responses (as obtained from Table I) are shown for Vq = 
20, 40 and 80 ft/sec and A^ = 9.66 ft/sec^. Note that the responses presented 
here have the same form as those in Fig. C-3; however, the peak amplitudes 
AV are markedly lower than the model predictions. In addition, the drive 
shaft "locked" momentarily during the first two seconds of the test at 80 ft/ 
sec causing the initial oscillatory behavior. 

Wheel slip occurred for Vq >. 40 ft/sec and Ac >. 12.88 ft/sec^, and the 
resulting anti-skid mode of response was highly oscillatory. Again, if a more 
efficient anti-skid mode had been employed, the model response would have been 
a reasonable approximation to the full-scale response. 
F. Conclusions 

A model has been specified for the bra king/ roadway Interface dynamics 
of a typical U.S. passenger sedan. The model parameters are functions of both 
velocity and acceleration rate, and the model is thus a nonlinear one. 

The responses obtained from this model, for the speed range 20-90 ft/sec 
and the acceleration range 6.44-14.5 ft/sec^, are reasonable approximations to 
corresponding full-scale responses under both wet- and dry-road conditions. 
However, as considerable variability was observed in the full-scale responses, 
and thus in the correlation between these and the model responses, the model 
should be employed with care. This variability can be accounted for via a 
change in gain, and thus when designing a closed-loop braking controller, one 

-178- 



5H 



AV 
(ft/sec) 



0- 




Full-scale response 

^ Model response 



Time(sec) 5 
a) Vq = 20 ft/sec. 




' ^ r 

Time (sec)5 



b) Vq = 40 ft/sec. 

Fin. C-10 Vehicle response for two selected initial 
speeds, Ac = 12.88 ft/sec^. V = V5 and 
vfet-pavernent conditions. 




Assumed full-scale response 
Model response 



I I 
Time(sec) 



T 



F1q» C-11 Assumed full-scale response* with an efficient 
anti-skid mode (Vq = 40 ft/sec, A^. = 12.88 
ft/sec^ amd v/et-pavement conditions. 



-179- 



AV 
(ft/sec) 5- 



X 



0- 



X ft »( 







AV 
(ft/sec) 







— Full-scale response 
X Model response 



T 1 'I 



T" 
5 



— I 1 — 

Tjme(sec) 



a) Vo « 20 ft/sec. 




Time(sec) 



b) Vo « 40 ft/sec. 







10 



Driveshaft locfked 




5 Tlme(sec) 
c) Vq « 80 ft/sec. 



Fig. C-12 Comparison between full-scale and model responses 
for V = V5, Ag » 9.66 ft/sec^, and wet-pavement. 



-180- 



one should insure that Its performance Is relatively insensitive to this change. 
The observed changes under full-scale conditions were some ±20% of the nominal 
value specified in Table C-I; thus, for a conservative choice one might design 
to accomodate changes of up to ±50%. 

An efficient anti-skid mode should be incorporated into the design so 
that adequate braking performance at rates up to 12.88 ft/sec^ could be achieved 
on both wet and dry pavement. The specified model could be employed in this 
part of the design, as it should provide a reasonable approximation to the res- 
ponse in a well -control led anti-skid mode. 

Finally, it should be emphasized that the model presented here was 
selected because of its simplicity and potential for use in the braking con- 
troller design process. Another model, with more accurate predictive properties, 
may readily be found; however, it seems certain that the latter will be charac- 
terized by a fairly complex, nonlinear differential equation. 



-181- 



APPENDIX D 
DIGITAL COMMAND GENERATION 



A. Introduction 

In an operational system, the command state (A^, V^. and X^.) for a con- 
trolled vehicle would only be available at discrete times t = nTs, where Tg 
is the sampling instant. In one attractive approach, which was described in 
Chapter II, Vc(nTs) and Xc(nTs) would be derived from A^CnTg) by appropriate 
processing onboard a controlled vehicle. 

The actual states (A, V, and X) could be continuously available, as 
was described in Chapter IV and, in terms of the position control of a vehicle, 
one would have the situation depicted in Fig. D-1. Here, to obtain a good 
approximation (AX*) to AX(t) = Xc(t) - X(t), the switch Si would be synchro- 
nized with the processing of Xc(nTs) so that 

AX* = [Xc(t) - X(t)]t=nTs- 
This quantity, after processing by a hold circuit, would be the primary input 
to the vehicle controller. In general, controller performance would be improved 
by also employing input(s) related to AcCnTg) and Vc(nTs) as shown. 

One realization of this configuration, which was intended for use with 
a crossed-wire information source, is discussed in this appendix. 

B. A Command Generator 

The command states Ac(nTs), V^CnTs) and X(nTs) could be computed by a 
general-purpose computer at either the sector or the vehicle level. However, the 
numerical computation of Vc and Xc from a given acceleration-command profile 
is a time-consuming operation which could tie up most of a general -purpose 



-182- 




01 



> 



■a 
a; 



o 

C 

o 
u 



-a 

I. 
«o 
o 

x: 
c 
o 

V) 

c 
o 



OJ 

c 
o 



o 

I. 

c 
o 
u 

■o 

<a 

L. 
0^ 
+J 

3 

a. 

E 
O 



-183- 



computer's processing capability. In many applications involving routine 
repetitive operations, special-purpose hardware,or possibly a dedicated micro- 
computer, would be a viable alternative. 

In the current study, special -purpose hardware was the most practical 
choice; thus, it was employed in the design and construction of a vehicle- 
borne command generator. This generator functions as follows: 
Command acceleration profiles are stored in memory 
as a block of binary words. The weighting of the least 
significant bit is qn ft/sec2, and the words are accessed 
from m«nory at intervals of Tg seconds. The resulting quan- 
tized acceleration profile is the basis for velocity and 
displacement computations. 

The integral of the typical quantized A^ft) function 
shown in Fig, D-2(a) is the series of dashed straight-line 
segments, identified as Vc(t) in Fig. D-2(b). Here Ac(t) 
over the ith interval is denoted by Ad* and Vj,(t) at the 
end of this interval by V^i. Note that 

n 

Vcn = Ts I Act (ft/sec) (D-1) 
i=l 

The second integral of Ac(t) is the continuous posi- 
tion function shown as a dashed line in Fig. D-2(c). A 
discrete displacement command (Xc(nTs) = Xcn)» which is 
equal to this function at the sampling instants, is readily 
obtained via a 3-part process: First, the area under the 
Vcn function (shown by the solid line in Fig. D-2(b)) is 
obtained as 

-184- 



1 Acceleration 








(ft/sec^) 






Ac4 






1 *. i^ 


i h-^s 




OAci 5l 




10 


— ». 



Ac6 



(a) 



.Velocity 
(ft/sec) 



VcSZj 

2L 



Vc 4 VcS 



Vc7lU 



Vc8 



"T 

10 

(b) 



— t 



OVcl 



Position 
(ft) 



Xc9 



Xc4 



Xc3jJ 



-^cZ 
/ 
/ 

Xc64_ 



Xcsij 



Xc8j 



X.(t) 



^ci 



10 
(c) 



Fin. n-2 A command acceleration profile and correspondinq 
velocity and position profiles. 

-185- 



n-1 

1=0 
Second, the "triangular" areas between the Vc(t) and Vp 
curves is computed as 

7^ I Act; 
"^ i=l 

and third, X^p is obtained via 

n-1 n 

Xcn = Ts I Vci + 1 Ts2 J ^^. (ft) (0-2) 
i=0 "^ i=0 

One hardware realization of these operations is depicted in Fig. D-3. 
The accelerations are binary coded, using the 2's complement representation 
for negative values. The weighting of the least significant acceleration bit 
is q/^ , and the number of bits required to represent acceleration is 

Na = log2 4^-U- . 

A 
'^c 

where ||A|| is the sum of the maximum magnitudes of positive and negative accele- 
ration. 

The quantity V^p is obtained from the Aq^- via an arithmatic accumulator, 
where the number of required bits is 

(Vc)max 



Hy = log2 



V^= 



Here, (Vc)max ^^ ^^^ maximum required command velocity in ft/ sec. 

The implementation of the X^n computation consists of an accumulator 

summing two inputs simultaneously. The derived velocity word is one input 

and, since the weighting factor (q^ ) of the x <0> bit isq Tg ft/sec, 

c \ 

-186- 




c 
o 



<o 



3 



U 



u 

X 

c 



o 



c 
o 

♦-> 

to 

c 
a; 



Q. 

E 

•r— 

c 
c: 



I 



en 

•r— 
U- 



J 



the first term of (D-2) is realized. The second Input Is derived from the 
acceleration word, shifted one bit-position tov/ard the least significant end, 
thereby halving the effective acceleration input. The number of bits required 
to implement the Xcn accumulator is 

Nx = logo ^^ , 

qxc 

where X^^ax ^s the maximum command distance and 



2 



^Xc = i <^Ac Ts' 



It is of interest to specify the required word sizes for a choice of 

parameters which might be expected in practice. For A^^gx ~ 25 ft/sec^, V^iax 

= 160 ft/sec, Xfuax = ^096 ft, q/\j. = 0.39 ft/sec^ and Tg = 0.1 sec, then 

Na = 7 bits, 

Nv = 12 bits, 
and 

Nx = 21 bits. 

C. Integration of Command and Information Source Signals 

When a crossed-wire information source is employed to obtain vehicle 
position, a discrete position signal Xyj is available each time a wire is crossed. 
The use of a position interpolator yields X, an estimate of the distance tra- 
veled between wires. Then Xy^ + X, when properly interpreted, is a continuously 
available position signal. 

Since Xc(t) = X^n at the command updating instant, AX* is derived by 
sampling and holding AX at this instant as is symbolically shown in Fig. D-4. 
Here, both Xc(nTs) and X^^ are in digital form (and both are capable of repre- 
senting displacements ranging from zero to some large number such as 4096 ft). 

-188- 



X^(nT^ )-X„-X 




sample at 

command— update instant 



Fig. n-4 Implementation of AX* for a crossed-wire information 
source with position interpolation. 



The only feasible means of obtaining 

Xc(nTs) - X,, 
is by using a binary subtractor. The result in a binary number, which even 
under extreme conditions, represents less than ±16 ft of position error (It 
is assumed that position errors larger than approximately 10 ft would repre- 
sent an abnormal condition and would require a sector shutdown). A binary 
number in this range can easily and economically be converted to a bipolar, 
analog voltage; X is then subtracted and the result is sampled and held. This 
approach was employed in a preliminary field evaluation of the crossed-wire 
information source/vehicle controller combination, which was conducted in the 
summer of 1976. 



-189- 



REFERENCES 



1. Ellas, S.E.G., "The West Virginia University--Morgantown Personal Rapid 

Transit System," in Personal Rapid Transit II , J.E. Anderson, 
Ed., University of Minnesota, Minneapolis, Minn,, Dec. 1973. 

2. Anon, Proceedings of the First International Conference on Dual-Mode 

Transportation , Washington, D.C., May 29-31, 1974. 

3. Gardels, K., "Automatic Car Controls for Electronic Highways," General 

Motors Research Laboratories, General Motors Corporation, 
Warren, Michigan, GMR-276, June 1960. 

4. TRW Systems Group, "Study of Synchronous Longitudinal Guidance as Applied 

to Intercity Automated Highway Networks," Final Report prepared 
for the Office of High Speed Transportation, Department of 
Transportation, September 1969. 

5. Stefanik, R.G., and Kiselewich, S.J., "Evaluation of the Operating Condi- 

tions of a Detriot Dual -Mode Vehicle Network," presented at the 
1972 SAE Automotive Engr. Congress, Jan. 1972, SAE Paper 720272. 

6. Wilson, D.G., Ed., "Automated Guideway Transportation Between and Within 

Cities," Urban Systems Laboratory Rpt. No. FRA-RT-72-14, Mass. 
Institute of Technology, Cambridge, Mass., Feb. 1971 (PB 206-269). 

7. Giles, G.C., and Martin, J. A., "Cable Installation for Vehicle Guidance 

Investigations in the New Research Track at Crowthorne," JAM 
Road Research Lab., Crowthorne, England, Rpt. RN/40 57/CGG. 

8. Oshima, Y., Kikuchi, E., Kimura, M., and Matsumoto, S., "Control System 

for Automobile Driving," Proceedings Tokyo IFAC Symposium . 
1965, pp. 347-357. 

9. Fenton, R.E., et al , "One Approach to Highway Automation," Proceedings of 

the IEEE , Vol. 46, No. 4, April 1968, pp. 556-566. 

10. Fenton, R.E., et al., "Advances Toward the Automatic Highway," Highway 

Research Record , No. 344, Washington, D.C., Jan. 1971, pp. 1-20. 

11. Fenton, R.E., and Olson, K.W., "An Investigation of Highway Automation," 

Rpt. EES 276-6, Dept. of Elec. Engr., The Ohio State University, 
Columbus, Ohio, March 1969. 

12. Anon., "An Investigation of Highway Automation," Rpt. EES 276A-12 Dept. 

of Elec. Engr., The Ohio State University, Cols., Ohio, April 1971. 



-190- 



References (Cont.) 



13. Fenton, R.E., Ed., "An Investigation of Highway Automation," Pept. Mo. 

276A-15, Dept. of Elec. Fngr., The Ohio State University, 
Columbus, Ohio, September 1974, 

14. "Practicality of Automated Highway Systems," Research Project with Calsoan 

Corp., Contract DOT-FH-1 1-8903, March 1976. 

15. Olson, K.W., et al., "Studies in Vehicle Automatic Lateral Control --Theory 

and Experiment," Appendix I to "An Investigation of Highway 
Automation," Rpt. 276A-16, Dept of Elec. Engr., The Ohio State 
University, Columbus, Ohio, September 1974. 

16. Fenton, R.E., Ed., "Fundamental Studies in the Automatic Longitudinal 

Control of Vehicles," Final Report on DOT-0S-40100, Trans- 
portation Control Laboratory, The Ohio State University, Cols., 
Ohio 43210, July 1975 (Available from MTis). 

17. Fenton, R.E. et al,, "Studies in Synchronous Longitudinal Control," 

Transportation Control Laboratory Pot. FES 276A-17, Dept. of 
Elec. Engr., The Ohio State University, Cols., Ohio 43210, 
Septenber 1974. 

18. Ries, Fdward and Cuccia, Louis C. "Status Report: Communications in Mass 

Transit Guided-Roadway Systems," Microwave Systems News (MSN) , 
Vol. 4, No. 6, Dec. /Jan. 1975, op. 34-42. 

19. Friedmann, W. and Peltzer N., "Linear Transmission of Information Between 

Track and Train by Means of High Frequency," Brown-Boveri Review , 
Sept. /Oct. 1965, pp. 752-760. 

20. Hahn, H.J., "Automatic Operation of Urban Rapid Transit and Underground 

Railv/ays," Drown-Boveri Review , Dec. 1971, pp. 553-565. 

21. Takahashi, K. , et al., "New Induction Radio System," Sumitomo Electric 

Technical Review , No. 13, Jan. 1970, pp. 29-33. 

22. Schwartz, M., Information Transmission, Modulation, and Noise (2nd Ed.), 

McGraw-Hill, Inc., New York, 1970. ' 

23. Peterson, W.W. and Weldon, E.J., Jr., Error-Correcting Codes , MIT Press, 

Cambridge, Massachusetts, 197X 

24. Stiffler, J.J., Theory of Synchronous Communications , Prentice-Hall, Inc., 

Eng 1 ewood Cliffs, New Jersey, 1971. 

25. Gelb, A.G., et al.. Applied Optimal Estimation , MIT Press, Cambridge, 

Massachusetts, 1974. 



-191- 



References (Cont.) 

26. Tsypkin, 1,7., Adaption and Learning in Automatic Systems , Academic Press, 

New York, 1971. 

27. D'Azzo, J.J., and Houpis, C.H., Feedback Control Systems Analysis and 

Synthesis . Second Edition, McGraw-Hill, New York, 1966. 

28. Mayhan, R.J., et al., "The Use of Enhancement Plates for Improved Doppler 

Radar Performance for Ground Transport Systems," Proceedings 
of the IEEE, Vol. 64, No. 11, November 1976, pp. 1644-1645. 

29. Bender, J.G., and Fenton, R.E., "On Vehicle Longitudinal Dynamics," in 

Traffic Flow and Transportation ," G.F. Newell, Ed., American 
Elsevier Publ. Co., Inc., New York, 1972, pp. 33-46. 



-192- au.S. GOVERNMENT PRINTING OFFICE: 1977 727-511/1068 1-3 





ft^ 



OV 
N> 



DOT LIBRARY 



ODossfl^3 




% 



R&D